A physical engine-based section steel column hoisting collision simulation method

Abstract

The present application relates to the technical field of physical engine, specifically to a type steel column hoisting collision simulation method based on a physical engine, comprising the following steps: constructing a scaffold rigid body node group according to the extracted tower crane hook space coordinates and the type steel column dynamic bounding box trajectory; comparing the type steel column dynamic bounding box trajectory with the boundary coordinates of the scaffold rigid body node group to obtain a geometric penetration amount. The present application continuously processes the beam element deformation stress tensor, the material yield threshold, the pure deformation strain term, the plastic reduction stiffness matrix and the local deformation dissipation energy, so that the scaffold damage degree can participate in the equivalent contact stiffness coefficient reduction, and then the collision contact force amplitude, the collision contact force vector, the node displacement increment, the scaffold damaged deformation coordinates and the type steel column collision response state form a closed loop mapping relationship, thereby improving the consistent expression ability of the hoisting collision simulation on local damage, contact force change and visual response.

Description

Technical Field

[0001] This invention relates to the field of physics engine technology, and in particular to a physics engine-based method for simulating collisions during the hoisting of steel columns. Background Technology

[0002] Physics engine technology involves digital modeling, calculation, and simulation of real-world physical behavior, typically focusing on rigid body motion, flexible body deformation, collision detection, contact response, constraint solving, friction damping, dynamic integration, spatial coordinate mapping, mass attribute configuration, external force loading, and boundary condition constraints.

[0003] Current physics engine technology typically revolves around rigid body motion, flexible body deformation, collision detection, contact response, constraint solving, friction damping, dynamic integration, and boundary condition constraints. In practice, it tends to perform generalized calculations of object position, velocity, mass, inertia, stiffness, damping, contact normal vector, and penetration. The contact relationship between colliding objects tends to remain at the level of geometric detection and dynamic response, making it difficult to incorporate parameters such as the material elastic modulus, material density, yield threshold, and local deformation energy dissipation of engineering components into the same continuous link. In construction hoisting scenarios, if contact response is triggered solely based on spatial position and penetration, when a steel column contacts a local member of the scaffolding, the force diffusion range of the scaffolding node may be simplified to a fixed neighborhood or the overall response, making it difficult to accurately represent local damage propagation, plastic reduction, and changes in contact stiffness. Therefore, improvements are needed. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a physics engine-based collision simulation method for steel column hoisting.

[0005] To achieve the above objectives, the present invention adopts the following technical solution: a physics engine-based collision simulation method for steel column hoisting, comprising the following steps:

[0006] Based on the extracted spatial coordinates of the tower crane hook and the dynamic bounding box trajectory of the steel column, a rigid body node group of the scaffolding is constructed.

[0007] By comparing the trajectory of the dynamic bounding box of the steel column with the boundary coordinates of the rigid body node group of the scaffold, the geometric penetration amount is obtained; when it is determined that the geometric penetration amount is greater than zero, the surface coordinate data and surface contact normal vector associated with the penetration area are extracted, and the initial collision contact point coordinates are generated based on the surface coordinate data.

[0008] The one-dimensional elastic stress wave velocity is calculated by using the elastic modulus and density of the scaffold material at the initial collision contact point coordinates.

[0009] Extract the cumulative collision time parameter from the moment of collision to the current calculation frame, and calculate the dynamic envelope radius by combining the one-dimensional elastic stress wave velocity with the cumulative collision time parameter.

[0010] A spatially extended sphere boundary is constructed with the initial collision contact point coordinates as the center and the dynamic envelope radius as the radius.

[0011] By comparing the spatial coordinates of the rigid body node group of the scaffold with the boundary of the spatial extended sphere, the state flag of the node located inside the boundary of the spatial extended sphere is changed from the zero-constraint rigid body value to the co-rotation node value, generating a local upgraded node group; the displacement vector of the node located outside the boundary of the spatial extended sphere is locked as the boundary constant of the current calculation frame.

[0012] By combining the local up-dimensional node group with the boundary constant, a dynamic collision computation domain is constructed.

[0013] Preferably, the method further includes:

[0014] Calculate the beam element deformation stress tensor associated with each node in the local upgraded node group; compare the beam element deformation stress tensor with the material yield threshold, and when the beam element deformation stress tensor is greater than the material yield threshold, obtain the pure deformation strain term; update the stiffness matrix of the dynamic collision calculation domain according to the pure deformation strain term to generate a plastic reduced stiffness matrix; calculate the local deformation dissipation energy according to the pure deformation strain term, the plastic reduced stiffness matrix, and the transpose of the pure deformation strain term.

[0015] A damage degradation factor is constructed based on the local deformation dissipation energy. This factor is then used to reduce the preset initial contact stiffness coefficient to obtain an equivalent contact stiffness coefficient. The relative velocity between the steel column and the scaffold rigid body node group at the initial collision contact point coordinates is extracted. The collision contact force amplitude is calculated by combining the geometric penetration, the relative velocity, the equivalent contact stiffness coefficient, and the preset contact damping coefficient. The collision contact force amplitude is then calculated by operating on the surface contact normal vector to generate a collision contact force vector. This vector is then substituted as an external excitation term into the dynamic equilibrium equation of the dynamic collision calculation domain to obtain the node displacement increment. The initial spatial coordinates of the scaffold rigid body node group are updated with the node displacement increment to generate the scaffold damaged deformation coordinates. The scaffold damaged deformation coordinates are mapped to the spatial displacement parameters of the steel column in the current calculation frame and then distributed as state change instructions in the rendering parameter register to obtain the steel column collision response state.

[0016] Preferably, the step of obtaining the one-dimensional elastic stress wave velocity is as follows:

[0017] Call the spatial coordinates of the tower crane hook, read the vertex coordinate sequence in the dynamic bounding box trajectory of the steel column frame by frame, map the vertex coordinate sequence to a unified spatial coordinate system, write the fixed constraint item according to the spatial positional relationship of the scaffold upright node, horizontal node and diagonal brace node, lock the node displacement degree of freedom marked by the fixed constraint item, and retain the spatial coordinate index of the unlocked node to form a rigid body node group of the scaffold.

[0018] Extract the boundary coordinates of the rigid body node group of the scaffold, compare the outer boundary coordinates of the dynamic bounding box trajectory of the steel column with the boundary coordinates of the rigid body node group of the scaffold frame by frame, calculate the overlap distance of the boundary coordinates in each direction, determine the value of the overlap distance that satisfies the positive intrusion relationship as the geometric penetration amount, when the geometric penetration amount is greater than zero, lock the surface coordinate data associated with the penetration area, extract the surface contact normal vector associated with the penetration area, and generate the initial collision contact point coordinates according to the spatial position aggregation center of the surface coordinate data;

[0019] Retrieve the scaffold member number corresponding to the initial collision contact point coordinates, read the elastic modulus of the scaffold material bound to the scaffold member number, read the material density bound to the scaffold member number, use the elastic modulus of the scaffold material as the numerator of the square root ratio, use the material density as the denominator of the square root ratio, and perform a square root operation on the ratio of the elastic modulus of the scaffold material and the material density to obtain the one-dimensional elastic stress wave velocity.

[0020] Preferably, the step of obtaining the dynamic envelope radius is as follows:

[0021] Read the frame number at the moment of collision, read the frame number of the current calculation frame, subtract the frame number at the moment of collision from the frame number of the current calculation frame, convert it into a cumulative collision time parameter according to the simulation frame interval, and multiply the one-dimensional elastic stress wave velocity with the cumulative collision time parameter to obtain the dynamic envelope radius.

[0022] Preferably, the step of obtaining the dynamic collision calculation domain is as follows:

[0023] The initial collision contact point coordinates are called and determined as the spatial sphere center coordinates. The dynamic envelope radius is determined as the spatial sphere expansion distance. According to the spatial coordinate system where the rigid body node group of the scaffold is located, the boundary positions in each direction around the spatial sphere center coordinates are marked to form the spatial expansion sphere boundary.

[0024] Based on the spatial extended sphere boundary, the spatial coordinates of each node in the rigid body node group of the scaffold are read one by one. The distance from the spatial coordinates of each node to the coordinates of the spatial sphere center is calculated. The status flag of the node whose distance is less than or equal to the dynamic envelope radius is changed from the zero-constraint rigid body value to the co-rotation node value, generating a local upgraded node group. The displacement vector of the node whose distance is greater than the dynamic envelope radius is locked as the boundary constant of the current calculation frame. The calculation boundary is established according to the node index of the local upgraded node group and the locking index of the boundary constant, forming a dynamic collision calculation domain.

[0025] Preferably, the step of obtaining the deformation stress tensor of the beam element is as follows:

[0026] The node index, spatial coordinates, and connection relationships of each node in the local upgraded node group are read one by one. The beam elements associated with each node are located according to the node connection relationships. The spatial coordinate difference between the two ends of the beam element in the current calculation frame is extracted. The axial expansion, bending angle change, and cross-sectional torsion change of the beam element are calculated. The axial expansion, bending angle change, and cross-sectional torsion change of the beam element are mapped to the local coordinate direction of the beam element to form the beam element deformation stress tensor.

[0027] Preferably, the step of obtaining the local deformation dissipation energy is as follows:

[0028] The axial stress component, bending stress component, and torsional stress component in the deformation stress tensor of the beam element are read item by item. Each stress component is compared with the material yield threshold. When any stress component is greater than the material yield threshold, the displacement matrix associated with the local upgraded node group is read. The matrix components generated by the overall translation and overall rotation in the displacement matrix are marked as large displacement components, and the matrix components generated by the beam element expansion, contraction, and torsion are marked as local deformation components. The large displacement components are removed from the displacement matrix and the local deformation components are retained to obtain the pure deformation strain term. According to the yield position index corresponding to the pure deformation strain term, the matrix elements with the same yield position index in the stiffness matrix of the dynamic collision calculation domain are reduced and updated to generate the plastic reduced stiffness matrix.

[0029] Read the row and column indices of the pure deformation strain term, transpose the pure deformation strain term according to the row and column indices to the transpose of the pure deformation strain term, perform a quadratic product operation on the pure deformation strain term, the plastic reduced stiffness matrix, and the transpose of the pure deformation strain term according to the same row and column indices, extract the spatial integral weight corresponding to each beam element in the dynamic collision calculation domain, and accumulate the quadratic product operation results item by item according to the spatial integral weights to obtain the local deformation dissipation energy.

[0030] Preferably, the step of obtaining the collision contact force vector is as follows:

[0031] Read the beam element number, yield position index, and spatial integral weight corresponding to the local deformation dissipation energy. Match the preset initial contact stiffness coefficient according to the beam element number. Convert the local deformation dissipation energy into a damage degradation factor. Use the damage degradation factor to reduce the preset initial contact stiffness coefficient to obtain an equivalent contact stiffness coefficient. Extract the velocity vector of the steel column and the velocity vector of the scaffold rigid body node group at the initial collision contact point coordinates. Calculate the difference between the velocity vector of the steel column and the velocity vector of the scaffold rigid body node group to obtain the relative motion velocity. Combine the geometric penetration amount, relative motion velocity, equivalent contact stiffness coefficient, and preset contact damping coefficient to calculate the collision contact force amplitude. Expand the collision contact force amplitude along the surface contact normal vector direction to generate the collision contact force vector.

[0032] Preferably, the step of obtaining the collision response state of the steel column is as follows:

[0033] Read the node index of the local upgraded node group, the locking index of the boundary constant, and the time step of the current calculation frame in the dynamic collision calculation domain. Write the collision contact force vector into the external excitation term according to the node index corresponding to the initial collision contact point coordinates. Substitute the external excitation term into the dynamic equilibrium equation of the dynamic collision calculation domain. Solve the node displacement change of the local upgraded node group item by item according to the time step of the current calculation frame to obtain the node displacement increment. Superimpose the node displacement increment on the initial spatial coordinates of the rigid body node group of the scaffold according to the same node index to generate the scaffold damaged deformation coordinates.

[0034] Read the spatial displacement parameters of the steel column in the current calculation frame, write the damaged deformation coordinates of the scaffolding into the rendering parameter register according to the node index of the scaffolding rigid body node group, write the spatial displacement parameters of the steel column in the current calculation frame into the rendering parameter register according to the steel column component index, check the writing status of the node index of the scaffolding rigid body node group and the steel column component index, and issue a status change command when the writing status is completed, and synchronously update the deformation display status corresponding to the damaged deformation coordinates of the scaffolding and the displacement display status corresponding to the spatial displacement parameters of the steel column in the current calculation frame to obtain the collision response status of the steel column.

[0035] Compared with the prior art, the advantages and positive effects of the present invention are as follows:

[0036] In this invention, a rigid body node group of scaffolding is constructed by using the spatial coordinates of the tower crane hook and the dynamic enclosing box trajectory of the steel column. Geometric penetration is obtained by comparing boundary coordinates, shifting collision judgment from simple spatial overlap identification to contact judgment with quantitative evidence of penetration depth. When the geometric penetration is greater than zero, surface coordinate data and surface contact normal vectors of the penetration area are further extracted to generate initial collision contact point coordinates, providing a clear spatial position and direction basis for subsequent contact force calculations. One-dimensional elastic stress wave velocity is calculated using the elastic modulus and density of the scaffolding material, and a dynamic envelope radius is formed by combining it with accumulated collision time parameters, allowing the collision influence range to expand over time, rather than fixedly selecting a neighboring area. A spatially expanded sphere is used... By filtering the rigid body node group of the scaffolding at the boundary, changing the internal nodes to co-rotating node values, and locking the displacement vector of the external nodes to the boundary constant of the current calculation frame, the dynamic collision calculation domain can take into account both local deformation accuracy and overall calculation stability. Through continuous processing of beam element deformation stress tensor, material yield threshold, pure deformation strain term, plastic reduced stiffness matrix, and local deformation dissipation energy, the degree of scaffolding damage can participate in the reduction of equivalent contact stiffness coefficient. This enables the collision contact force amplitude, collision contact force vector, node displacement increment, scaffolding damaged deformation coordinates, and steel column collision response state to form a closed-loop mapping relationship, improving the consistent expression ability of hoisting collision simulation of local damage, contact force changes, and visual response. Attached Figure Description

[0037] Figure 1 This is a graph showing the change of the dynamic envelope radius over the cumulative collision time. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0039] Please see Figure 1 This invention provides a technical solution: a physics engine-based collision simulation method for hoisting steel columns, comprising the following steps:

[0040] Based on the extracted spatial coordinates of the tower crane hook and the dynamic bounding box trajectory of the steel column, a rigid body node group of the scaffold is constructed. The boundary coordinates of the dynamic bounding box trajectory of the steel column and the rigid body node group of the scaffold are compared to obtain the geometric penetration amount. When the geometric penetration amount is determined to be greater than zero, the surface coordinate data and surface contact normal vector associated with the penetration area are extracted, and the initial collision contact point coordinates are generated based on the surface coordinate data. The elastic modulus and material density of the scaffold material at the initial collision contact point coordinates are used to calculate the one-dimensional elastic stress wave velocity.

[0041] The cumulative collision time parameters from the moment of collision to the current calculation frame are extracted. The one-dimensional elastic stress wave velocity is calculated with the cumulative collision time parameters to obtain the dynamic envelope radius. A spatially extended sphere boundary is constructed with the initial collision contact point coordinates as the center and the dynamic envelope radius as the radius. The spatial coordinates of the scaffold rigid body node group are compared with the spatially extended sphere boundary. The state flags of the nodes located inside the spatially extended sphere boundary are changed from zero-constraint rigid body values ​​to co-rotation node values, generating a locally upgraded node group. The displacement vectors of the nodes located outside the spatially extended sphere boundary are locked as boundary constants of the current calculation frame. The dynamic collision calculation domain is constructed by combining the locally upgraded node group and the boundary constants.

[0042] Calculate the deformation stress tensor of beam elements associated with each node in the local upgraded node group; compare the deformation stress tensor of beam elements with the material yield threshold, and obtain the pure deformation strain term when the deformation stress tensor of beam elements is greater than the material yield threshold; update the stiffness matrix of the dynamic collision calculation domain according to the pure deformation strain term to generate the plastic reduced stiffness matrix; calculate the local deformation dissipation energy according to the pure deformation strain term, the plastic reduced stiffness matrix, and the transpose of the pure deformation strain term.

[0043] A damage degradation factor is constructed based on the local deformation dissipation energy. This factor is then used to reduce the preset initial contact stiffness coefficient, yielding an equivalent contact stiffness coefficient. The relative velocity between the steel column and the rigid scaffold node group at the initial collision contact point coordinates is extracted. The collision contact force amplitude is calculated by combining the geometric penetration, relative velocity, equivalent contact stiffness coefficient, and preset contact damping coefficient. The collision contact force amplitude is then calculated using the surface contact normal vector to generate a collision contact force vector. This force vector is then substituted as an external excitation term into the dynamic equilibrium equations of the dynamic collision calculation domain to obtain the node displacement increment. The initial spatial coordinates and node displacement increments of the rigid scaffold node group are updated to generate the scaffold damaged deformation coordinates. The scaffold damaged deformation coordinates and the spatial displacement parameters of the steel column in the current calculation frame are mapped to the rendering parameter register for state change instruction distribution, resulting in the steel column collision response state.

[0044] The steps for obtaining the one-dimensional elastic stress wave velocity are as follows:

[0045] Call the spatial coordinates of the tower crane hook, read the vertex coordinate sequence in the dynamic bounding box trajectory of the steel column frame by frame, map the vertex coordinate sequence to a unified spatial coordinate system, write the fixed constraint item according to the spatial positional relationship of the scaffold upright node, horizontal node and diagonal brace node, lock the node displacement degree of freedom marked by the fixed constraint item, and retain the spatial coordinate index of the unlocked node to form a rigid body node group of the scaffold.

[0046] Extract the boundary coordinates of the rigid body node group of the scaffold, compare the outer boundary coordinates of the dynamic bounding box trajectory of the steel column with the boundary coordinates of the rigid body node group of the scaffold frame by frame, calculate the overlap distance of the boundary coordinates in each direction, determine the value of the overlap distance that satisfies the positive intrusion relationship as the geometric penetration amount, when the geometric penetration amount is greater than zero, lock the surface coordinate data associated with the penetration area, extract the surface contact normal vector associated with the penetration area, and generate the initial collision contact point coordinates according to the spatial position aggregation center of the surface coordinate data.

[0047] Retrieve the scaffold member number corresponding to the initial collision contact point coordinates, read the elastic modulus of the scaffold material bound to the scaffold member number, read the material density bound to the scaffold member number, use the elastic modulus of the scaffold material as the numerator of the square root ratio, use the material density as the denominator of the square root ratio, and perform a square root operation on the ratio of the elastic modulus of the scaffold material and the material density to obtain the one-dimensional elastic stress wave velocity.

[0048] Specifically, the spatial coordinates of the tower crane hook are invoked. By reading the 3D model data of the steel column and the motion trajectory of the tower crane hook frame by frame, the vertex coordinate sequence in the dynamic bounding box trajectory of the steel column in each frame is calculated. Then, a unified spatial coordinate system is established with a fixed reference point in the construction site (such as the corner point of the building's foundation) as the origin. The vertex coordinate sequence is transformed from its local coordinate system to this unified spatial coordinate system. Next, a pre-established 3D geometric model of the scaffolding is imported. This model defines in detail the precise spatial positions and connection relationships of all uprights, horizontal bars, and diagonal braces. Based on this model, the displacement values ​​of the six degrees of freedom (three translational degrees of freedom and three rotational degrees of freedom) of all bottom nodes connected to the ground or main structure are set to zero and marked as fixed constraints. For all other nodes in the model except for the fixed constraints, a unique spatial coordinate index and initial coordinate value are created and retained. Each unlocked node is regarded as an active node with six degrees of freedom. Finally, all these unlocked nodes and their associated initial coordinates and degrees of freedom states together form the rigid body node group of the scaffolding for subsequent collision simulation.

[0049] The overall outer boundary coordinates of the rigid body node group of the scaffold are extracted. Simultaneously, for preliminary coarse collision detection, a safety redundancy distance is added to the outer boundary coordinates of the dynamic bounding box trajectory of the steel column in each of the six directions (+X, -X, +Y, -Y, +Z, -Z). This distance is set according to the hoisting speed and simulation frame rate. For example, for a hoisting speed of 0.5 m / s and a simulation frequency of 50 Hz, with a displacement of 0.01 m per frame, a safety redundancy distance of 0.05 m can be set. Then, frame-by-frame, axis-aligned bounding box (AABB) intersection tests are performed on the outer boundary coordinates of the steel column and the boundary coordinates of the scaffold. The overlap distances in the X, Y, and Z axes are calculated. When the overlap distances in all three axes are greater than a preset zero threshold (e.g., greater than a floating-point precision error of 1E-6 meters), a collision is determined to have occurred. The minimum of the three overlapping distances is determined as the geometric penetration. Once the geometric penetration is determined to be greater than zero, a more precise intersection test (e.g., triangle-cylinder intersection test) is performed on the surface of the steel column and each member model of the scaffolding within the overlapping area. The coordinate data of all scaffolding member surfaces and steel column surfaces that actually come into contact are locked. Then, the average normal vector of each scaffolding member surface in the contact area is calculated and used as the surface contact normal vector. Finally, the geometric center point of all locked contact surface coordinate data is calculated and used as the initial collision contact point coordinates of this collision event.

[0050] The scaffold member number corresponding to the initial collision contact point coordinates is retrieved by performing a spatial nearest neighbor search within the rigid body node group of the scaffold. This involves calculating the distance from the initial collision contact point to the centerline of each member, identifying the member with the smallest distance as the colliding member, and obtaining its unique number. Subsequently, a pre-configured material property database is accessed, storing material parameters corresponding to scaffold members of different numbers or types. Using the colliding member's number as an index, its associated material properties are retrieved from the database, specifically including the elastic modulus and density of the scaffold material. For example, for commonly used Q235 steel, its elastic modulus... The typical value is 206 gigapascals ( ), material density The typical value is 7850 kg / m³. Then, based on the one-dimensional wave theory in solid mechanics, the propagation speed of the stress wave in the rod is calculated. This calculation is completed using the following formula:

[0051] ;

[0052] in, This is the final one-dimensional elastic stress wave velocity, measured in meters per second. It is the elastic modulus of scaffolding materials read from the database. The material density was read from the database. Substituting the example value of Q235 steel mentioned above, the one-dimensional elastic stress wave velocity was calculated to be approximately 5120 m / s. This velocity value will be used to determine the range of the dynamic region affected by the collision in subsequent calculations.

[0053] The steps to obtain the dynamic envelope radius are as follows:

[0054] Read the frame number at the moment of collision, read the frame number of the current calculation frame, subtract the frame number at the moment of collision from the frame number of the current calculation frame, convert it into a cumulative collision time parameter according to the simulation frame interval, and multiply the one-dimensional elastic stress wave velocity with the cumulative collision time parameter to obtain the dynamic envelope radius.

[0055] Specifically, the sequence number of the simulation frame in the collision detection step that first determines the geometric penetration to be greater than zero is read and recorded as the frame number at the moment of collision. At the same time, obtain the frame number of the simulation calculation currently in progress. The number of frames that the collision occurred in is obtained by calculating the difference between the two frame numbers. Then multiply this number of consecutive frames by the preset simulation time step (i.e., the simulation frame interval). ), calculate the cumulative collision time parameter from the start of the collision to the current moment. The simulation frame interval The setting needs to balance computational accuracy and efficiency. For high-speed collision simulations, it is usually set to a very small value. For example, if the simulation goal is to capture microsecond-level responses, Can be set to If the time is seconds, then the cumulative collision time parameter is calculated as follows: Next, the one-dimensional elastic stress wave velocity calculated in the previous step is... With this cumulative collision time parameter The physical meaning of performing a product operation is to calculate the farthest distance that an elastic wave can travel from the initial collision point; this distance is the dynamic envelope radius. Its calculation formula is This radius defines an influence area centered on the initial collision point, resulting in the dynamic envelope radius.

[0056] The steps for obtaining the dynamic collision computation domain are as follows:

[0057] The initial collision contact point coordinates are called and determined as the spatial sphere center coordinates. The dynamic envelope radius is determined as the spatial sphere expansion distance. According to the spatial coordinate system where the rigid body node group of the scaffold is located, the boundary positions in each direction around the spatial sphere center coordinates are marked to form the spatial expansion sphere boundary.

[0058] Based on the spatially extended sphere boundary, the spatial coordinates of each node in the rigid body node group of the scaffold are read one by one. The distance from the spatial coordinates of each node to the coordinates of the spatial sphere center is calculated. The status flag of the node whose distance is less than or equal to the dynamic envelope radius is changed from the zero-constraint rigid body value to the co-rotation node value, generating a local upgraded node group. The displacement vector of the node whose distance is greater than the dynamic envelope radius is locked as the boundary constant of the current calculation frame. The calculation boundary is established according to the node index of the local upgraded node group and the locking index of the boundary constant, forming a dynamic collision calculation domain.

[0059] Specifically, the initial collision contact point coordinates determined in the preceding steps are called, and these three-dimensional coordinates are... The coordinates of the sphere's center are directly specified as those for subsequent spatial partitioning operations. Simultaneously, the dynamic envelope radius calculated in the previous step is used. The coordinates of the sphere's center and the outer radius are set as the outer distance of the spatial sphere. Based on these coordinates, a virtual spatial expansion sphere is defined in the unified three-dimensional spatial coordinate system where the rigid body nodes of the scaffold are located. The boundary of this sphere consists of all points whose distance from the center is equal to the dynamic envelope radius. In practice, it is not necessary to generate a complete spherical mesh. Instead, the boundary is implicitly defined by recording the center coordinates and radius values. Subsequently, when determining node affiliation, the system will use these center coordinates and radius values ​​as the basis for judgment and mark the boundary positions in all directions around the spatial sphere's center coordinates. Its function is to create a dynamic, time-expanding sphere of influence. All scaffold structure parts falling within this sphere will be considered to be potentially affected by collision events, thus requiring more refined mechanical calculations, ultimately forming the boundary of the spatial expansion sphere.

[0060] Based on the coordinates of the sphere's center and the dynamic envelope radius defined by the spatially extended sphere boundary, traverse each node in the rigid body node group of the scaffolding and read the spatial coordinates of each node. And calculate its coordinates to the center of the sphere in space. Euclidean distance Then, the calculated distance With the current dynamic envelope radius If a comparison is made, If the node is located within the collision influence zone, its status flag is changed from "0" (representing an inactive rigid body state) to "1" (representing a co-rotating node participating in deformation calculations). The set of all nodes whose status flags are changed to "1" constitutes the local upscaling node group. (For distance...) Greater than the dynamic envelope radius For nodes that are not affected by the collision stress wave, their displacement and rotation vectors are locked in the current calculation frame, and they are not allowed to change in subsequent iterations. These locked displacement values ​​become the boundary constants of the current calculation step. Finally, the degrees of freedom to be solved defined by the node index of the local upgraded node group and the fixed boundary conditions defined by the locked index of the boundary constants are integrated to establish a greatly reduced-scale calculation model that only contains the affected region, forming a dynamic collision calculation domain.

[0061] The steps for obtaining the deformation stress tensor of a beam element are as follows:

[0062] The node index, spatial coordinates, and connection relationships of each node in the local upgraded node group are read one by one. The beam elements associated with each node are located according to the node connection relationships. The spatial coordinate difference between the two ends of the beam element in the current calculation frame is extracted. The axial expansion, bending angle change, and cross-sectional torsion change of the beam element are calculated. The axial expansion, bending angle change, and cross-sectional torsion change of the beam element are mapped to the local coordinate direction of the beam element to form the beam element deformation stress tensor.

[0063] Specifically, the unique index, current spatial coordinates, and predefined node connection relationship data table of each node in the local upscaling node group are read one by one. This data table clarifies which two nodes constitute a beam element. Based on this connection relationship, all beam elements whose two-end nodes belong to the local upscaling node group are located and traversed. For each beam element, the spatial coordinates of its two-end nodes after the update in the current calculation frame are extracted, the distance between these two coordinate points is calculated, and compared with the original length of the beam element during model initialization to obtain the axial expansion of the beam element. At the same time, by comparing the changes in the pose quaternions or rotation matrices of the two-end nodes in the local coordinate system of the beam element, the perpendicularity to the beam element is calculated. The changes in bending angle along the beam axis and the changes in cross-sectional torsion around the beam axis are calculated. Then, these deformations (axial expansion, bending angle, and torsional angle) calculated in the global coordinate system are uniformly mapped to the local coordinate system of the beam element with the beam element's own axis as the x-axis and the principal axes of the cross-section as the y and z axes through a coordinate transformation matrix. Using the constitutive relations of the material (for example, Hooke's law for the elastic stage), these deformations in the local coordinate system are converted into corresponding stress components. Finally, the calculated axial normal stress, the normal stress caused by bending, and the shear stress caused by torsion are combined to form the beam element deformation stress tensor describing the internal stress state of the beam element.

[0064] The steps for obtaining energy dissipated by local deformation are as follows:

[0065] The axial stress components, bending stress components, and torsional stress components in the deformation stress tensor of the beam element are read item by item. Each stress component is compared with the material yield threshold. When any stress component is greater than the material yield threshold, the displacement matrix associated with the local upgraded node group is read. The matrix components generated by the overall translation and overall rotation in the displacement matrix are marked as large displacement components, and the matrix components generated by the beam element expansion, contraction, and torsion are marked as local deformation components. The large displacement components are removed from the displacement matrix and the local deformation components are retained to obtain the pure deformation strain term. According to the yield position index corresponding to the pure deformation strain term, the matrix elements with the same yield position index in the stiffness matrix of the dynamic collision calculation domain are reduced and updated to generate the plastic reduced stiffness matrix.

[0066] Read the row and column indices of the pure deformation strain term, transpose the pure deformation strain term according to the row and column indices to the transpose of the pure deformation strain term, perform a quadratic product operation on the pure deformation strain term, the plastic reduced stiffness matrix, and the transpose of the pure deformation strain term according to the same row and column indices, extract the spatial integral weight corresponding to each beam element in the dynamic collision calculation domain, and accumulate the quadratic product operation results item by item according to the spatial integral weights to obtain the local deformation dissipation energy.

[0067] Specifically, the axial stress components, bending stress components, and torsional stress components located at the Gaussian integration points in the deformation stress tensor of the beam element are read item by item. Using the Von Mises yield criterion, these multiaxial stress components are combined into an equivalent stress. Then, the equivalent stress is compared with a preset material yield threshold. The comparison is performed, and this threshold is directly taken from the material property database. For example, for Q235 steel, Set to 235 megapascals, when determining When the integral point enters the plastic state, the nodal displacement matrix of the local upgraded node group associated with the beam element is read. Using the co-rotation coordinate method, the total displacement is decomposed into rigid body displacement (generated by overall translation and rotation) and local deformation displacement (generated by the beam element's own expansion, contraction, and torsion). The rigid body displacement component is removed from the total displacement matrix, and only the local deformation displacement that can cause changes in internal force is retained. This is then converted into a pure deformation strain term. Based on the location index of the integral point where yielding occurs, the matrix elements related to the contribution of that integral point in the overall stiffness matrix of the dynamic collision calculation domain are located. These matrix elements are then reduced according to a preset plasticity model (such as ideal elastoplastic or bilinear hardening model). For example, in the ideal elastoplastic model, the stiffness term related to the plastic flow direction can be multiplied by a reduction factor close to zero (such as 0.01) to generate a plastic reduced stiffness matrix that reflects the decrease in material stiffness.

[0068] Read the pure deformation strain term obtained in the previous step, which contains only the plastic deformation component. and its corresponding row and column indices, and generate its transpose. At the same time, the updated plastic reduced stiffness matrix is ​​invoked. Then, perform the quadratic product operation. In finite element theory, this operation represents the elastoplastic strain energy stored in an element within an incremental step. Next, to calculate the total dissipated energy of the entire dynamic collision computational domain, the energy of each beam element undergoing plastic deformation needs to be accumulated. This process is achieved through numerical integration, specifically by extracting the spatial integration weights corresponding to the preset Gaussian integration points within each beam element in the dynamic collision computational domain. And Jacobian matrix determinant The quadratic product calculated at each integration point is multiplied by its corresponding spatial integration weight and Jacobian determinant to obtain the local deformation dissipation energy contributed by that integration point in one increment step. Finally, the energy contribution values ​​calculated at all Gaussian integration points of all beam elements undergoing plastic deformation in the dynamic collision computation domain are summed to obtain the total energy dissipated due to material plastic deformation in the current time step, i.e., the local deformation dissipation energy.

[0069] The steps to obtain the collision contact force vector are as follows:

[0070] Read the beam element number, yield position index, and spatial integral weight corresponding to the local deformation dissipation energy. Match the preset initial contact stiffness coefficient according to the beam element number. Convert the local deformation dissipation energy into a damage degradation factor. Use the damage degradation factor to reduce the preset initial contact stiffness coefficient to obtain the equivalent contact stiffness coefficient. Extract the velocity vector of the steel column and the velocity vector of the scaffold rigid body node group at the initial collision contact point coordinates. Calculate the difference between the velocity vector of the steel column and the velocity vector of the scaffold rigid body node group to obtain the relative motion velocity. Combine the geometric penetration amount, relative motion velocity, equivalent contact stiffness coefficient, and preset contact damping coefficient to calculate the collision contact force amplitude. Expand the collision contact force amplitude along the surface contact normal vector direction to generate the collision contact force vector.

[0071] Specifically, the damage state of each beam element is read from the accumulated energy dissipated by local deformation, and the energy value is converted into a dimensionless damage degradation factor according to a preset damage evolution model. The value of this factor ranges from 0 to 1, where 0 represents no damage and 1 represents complete failure. For example, an energy-based damage model can be used. ,in It is the accumulated energy dissipated by local deformation, and This is the critical dissipation energy threshold of the material, which is calibrated using experimental data on the material's fracture toughness. For example, for a Q235 steel component of a specific size, it can be set to 50 joules. Then, this damage degradation factor is used to adjust the preset initial contact stiffness coefficient. After reduction, the equivalent contact stiffness coefficient is obtained. ,in Based on the geometric and material properties of the contact element, for example, set to 10% of the axial stiffness of the contacted member, a contact model based on a penalty function is then used to calculate the collision contact force amplitude. This force amplitude consists of an elastic term and a damping term, and is calculated as follows: ,in It is geometric penetration. It is the normal relative velocity between the steel column and the scaffold at the point of contact. This is the contact damping coefficient, which is set to dissipate contact energy and can be set as a percentage of the critical damping, for example... ,in Assuming the effective mass of the contacting bodies, the final calculated collision contact force amplitude is... Contact normal vector with surface Perform calculations to generate a collision contact force vector with a direction opposite to the normal vector. .

[0072] The steps for obtaining the collision response state of a steel column are as follows:

[0073] Read the node index of the local upgraded node group, the locking index of the boundary constant, and the time step of the current calculation frame in the dynamic collision calculation domain. Write the collision contact force vector into the external excitation term according to the node index corresponding to the initial collision contact point coordinates. Substitute the external excitation term into the dynamic equilibrium equation of the dynamic collision calculation domain. Solve the node displacement change of the local upgraded node group item by item according to the time step of the current calculation frame to obtain the node displacement increment. Superimpose the node displacement increment on the initial spatial coordinates of the rigid body node group of the scaffold according to the same node index to generate the scaffold damaged deformation coordinates.

[0074] Read the spatial displacement parameters of the steel column in the current calculation frame, write the damaged deformation coordinates of the scaffolding into the rendering parameter register according to the node index of the scaffolding rigid body node group, write the spatial displacement parameters of the steel column in the current calculation frame into the rendering parameter register according to the steel column component index, check the writing status of the node index of the scaffolding rigid body node group and the steel column component index, and issue a status change command when the writing status is completed, and synchronously update the deformation display status corresponding to the damaged deformation coordinates of the scaffolding and the displacement display status corresponding to the spatial displacement parameters of the steel column in the current calculation frame to obtain the collision response status of the steel column.

[0075] Specifically, it reads the complete definition of the dynamic collision computation domain, including the node index list of the local up-dimensional node group, the locking index list of the boundary constants, and the time step of the current computation frame. The collision contact force vector generated in the previous step is then applied to the external excitation term of the system's dynamic equilibrium equations according to the node index associated with its point of application (i.e., the initial collision contact point). In this context, the dynamic equilibrium equation is: ,in , , These are the mass matrix, damping matrix, and plastic reduced stiffness matrix of the dynamic collision computational domain, respectively. Then, an explicit time integration algorithm, such as the central difference method, is used to solve the equation within one time step. Within the local up-dimensional node group, based on the force and state at the current moment, the acceleration, velocity, and displacement changes of all nodes are calculated, resulting in the displacement increment vector of each active node. For nodes outside the dynamic collision calculation domain, their displacement increment is zero. Finally, the initial spatial coordinates of all nodes in the rigid body node group of the scaffold are vector-added with their corresponding cumulative displacement increments (the sum of all displacement increments from the start of the collision to the current frame) to update the three-dimensional coordinates of all nodes and generate scaffold damaged deformation coordinates that can reflect the damage and deformation state of the structure after the collision.

[0076] Read the updated spatial displacement parameters of the steel column in the current calculation frame due to the collision reaction force, including the three-dimensional coordinates of its centroid and the quaternions describing its attitude. Simultaneously, write the scaffolding damage deformation coordinate data generated in the previous step into a batch of rendering parameter registers (e.g., the vertex buffer object VBO of the graphics processing unit) dedicated to the graphics rendering pipeline, according to the original index of each node in the scaffolding rigid body node group. Correspondingly, write the updated spatial displacement parameters of the steel column into the same rendering parameter register according to its component index. After completing the data update, set a [missing information - likely a specific parameter register]. A step flag is used to notify the rendering thread that the data has been updated. For example, a boolean value of "data changed" is set from false to true. At the beginning of each frame's drawing loop, the rendering engine checks this flag. When the flag is detected as true, a state change instruction is immediately dispatched. This instruction commands the graphics processing unit to redraw the scene using the latest vertex coordinate data in the registers. This allows the damaged deformation state of the scaffolding and the displacement and attitude changes of the steel columns to be synchronously and accurately visualized on the display device, resulting in the final collision response state of the steel columns.

[0077] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A physics engine-based collision simulation method for hoisting steel columns, characterized in that, Includes the following steps: Based on the extracted spatial coordinates of the tower crane hook and the dynamic bounding box trajectory of the steel column, a rigid body node group of the scaffolding is constructed. By comparing the trajectory of the dynamic bounding box of the steel column with the boundary coordinates of the rigid body node group of the scaffold, the geometric penetration amount is obtained; when it is determined that the geometric penetration amount is greater than zero, the surface coordinate data and surface contact normal vector associated with the penetration area are extracted, and the initial collision contact point coordinates are generated based on the surface coordinate data. The one-dimensional elastic stress wave velocity is calculated by using the elastic modulus and density of the scaffold material at the initial collision contact point coordinates. Extract the cumulative collision time parameter from the moment of collision to the current calculation frame, and calculate the dynamic envelope radius by combining the one-dimensional elastic stress wave velocity with the cumulative collision time parameter. A spatially extended sphere boundary is constructed with the initial collision contact point coordinates as the center and the dynamic envelope radius as the radius. By comparing the spatial coordinates of the rigid body node group of the scaffold with the boundary of the spatial extended sphere, the state flag of the node located inside the boundary of the spatial extended sphere is changed from the zero-constraint rigid body value to the co-rotation node value, generating a local upgraded node group; the displacement vector of the node located outside the boundary of the spatial extended sphere is locked as the boundary constant of the current calculation frame. By combining the local up-dimensional node group with the boundary constant, a dynamic collision computation domain is constructed.

2. The collision simulation method for steel column hoisting based on a physics engine according to claim 1, characterized in that, The method further includes: Calculate the beam element deformation stress tensor associated with each node in the local upgraded node group; compare the beam element deformation stress tensor with the material yield threshold, and when the beam element deformation stress tensor is greater than the material yield threshold, obtain the pure deformation strain term; update the stiffness matrix of the dynamic collision calculation domain according to the pure deformation strain term to generate a plastic reduced stiffness matrix; calculate the local deformation dissipation energy according to the pure deformation strain term, the plastic reduced stiffness matrix, and the transpose of the pure deformation strain term. A damage degradation factor is constructed based on the local deformation dissipation energy. This factor is then used to reduce the preset initial contact stiffness coefficient to obtain an equivalent contact stiffness coefficient. The relative velocity between the steel column and the scaffold rigid body node group at the initial collision contact point coordinates is extracted. The collision contact force amplitude is calculated by combining the geometric penetration, the relative velocity, the equivalent contact stiffness coefficient, and the preset contact damping coefficient. The collision contact force amplitude is then calculated by operating on the surface contact normal vector to generate a collision contact force vector. This vector is then substituted as an external excitation term into the dynamic equilibrium equation of the dynamic collision calculation domain to obtain the node displacement increment. The initial spatial coordinates of the scaffold rigid body node group are updated with the node displacement increment to generate the scaffold damaged deformation coordinates. The scaffold damaged deformation coordinates are mapped to the spatial displacement parameters of the steel column in the current calculation frame and then distributed as state change instructions in the rendering parameter register to obtain the steel column collision response state.

3. The collision simulation method for steel column hoisting based on a physics engine according to claim 1, characterized in that, The steps for obtaining the one-dimensional elastic stress wave velocity are as follows: Call the spatial coordinates of the tower crane hook, read the vertex coordinate sequence in the dynamic bounding box trajectory of the steel column frame by frame, map the vertex coordinate sequence to a unified spatial coordinate system, write the fixed constraint item according to the spatial positional relationship of the scaffold upright node, horizontal node and diagonal brace node, lock the node displacement degree of freedom marked by the fixed constraint item, and retain the spatial coordinate index of the unlocked node to form a rigid body node group of the scaffold. Extract the boundary coordinates of the rigid body node group of the scaffold, compare the outer boundary coordinates of the dynamic bounding box trajectory of the steel column with the boundary coordinates of the rigid body node group of the scaffold frame by frame, calculate the overlap distance of the boundary coordinates in each direction, determine the value of the overlap distance that satisfies the positive intrusion relationship as the geometric penetration amount, when the geometric penetration amount is greater than zero, lock the surface coordinate data associated with the penetration area, extract the surface contact normal vector associated with the penetration area, and generate the initial collision contact point coordinates according to the spatial position aggregation center of the surface coordinate data; Retrieve the scaffold member number corresponding to the initial collision contact point coordinates, read the elastic modulus of the scaffold material bound to the scaffold member number, read the material density bound to the scaffold member number, use the elastic modulus of the scaffold material as the numerator of the square root ratio, use the material density as the denominator of the square root ratio, and perform a square root operation on the ratio of the elastic modulus of the scaffold material and the material density to obtain the one-dimensional elastic stress wave velocity.

4. The collision simulation method for steel column hoisting based on a physics engine according to claim 1, characterized in that, The steps for obtaining the dynamic envelope radius are as follows: Read the frame number at the moment of collision, read the frame number of the current calculation frame, subtract the frame number at the moment of collision from the frame number of the current calculation frame, convert it into a cumulative collision time parameter according to the simulation frame interval, and multiply the one-dimensional elastic stress wave velocity with the cumulative collision time parameter to obtain the dynamic envelope radius.

5. The collision simulation method for steel column hoisting based on a physics engine according to claim 1, characterized in that, The steps for obtaining the dynamic collision calculation domain are as follows: The initial collision contact point coordinates are called and determined as the spatial sphere center coordinates. The dynamic envelope radius is determined as the spatial sphere expansion distance. According to the spatial coordinate system where the rigid body node group of the scaffold is located, the boundary positions in each direction around the spatial sphere center coordinates are marked to form the spatial expansion sphere boundary. Based on the spatial extended sphere boundary, the spatial coordinates of each node in the rigid body node group of the scaffold are read one by one. The distance from the spatial coordinates of each node to the coordinates of the spatial sphere center is calculated. The status flag of the node whose distance is less than or equal to the dynamic envelope radius is changed from the zero-constraint rigid body value to the co-rotation node value, generating a local upgraded node group. The displacement vector of the node whose distance is greater than the dynamic envelope radius is locked as the boundary constant of the current calculation frame. The calculation boundary is established according to the node index of the local upgraded node group and the locking index of the boundary constant, forming a dynamic collision calculation domain.

6. The collision simulation method for steel column hoisting based on a physics engine according to claim 2, characterized in that, The steps for obtaining the deformation stress tensor of the beam element are as follows: The node index, spatial coordinates, and connection relationships of each node in the local upgraded node group are read one by one. The beam elements associated with each node are located according to the node connection relationships. The spatial coordinate difference between the two ends of the beam element in the current calculation frame is extracted. The axial expansion, bending angle change, and cross-sectional torsion change of the beam element are calculated. The axial expansion, bending angle change, and cross-sectional torsion change of the beam element are mapped to the local coordinate direction of the beam element to form the beam element deformation stress tensor.

7. The collision simulation method for steel column hoisting based on a physics engine according to claim 2, characterized in that, The steps for obtaining the energy dissipated by the local deformation are as follows: The axial stress component, bending stress component, and torsional stress component in the deformation stress tensor of the beam element are read item by item. Each stress component is compared with the material yield threshold. When any stress component is greater than the material yield threshold, the displacement matrix associated with the local upgraded node group is read. The matrix components generated by the overall translation and overall rotation in the displacement matrix are marked as large displacement components, and the matrix components generated by the beam element expansion, contraction, and torsion are marked as local deformation components. The large displacement components are removed from the displacement matrix and the local deformation components are retained to obtain the pure deformation strain term. According to the yield position index corresponding to the pure deformation strain term, the matrix elements with the same yield position index in the stiffness matrix of the dynamic collision calculation domain are reduced and updated to generate the plastic reduced stiffness matrix. Read the row and column indices of the pure deformation strain term, transpose the pure deformation strain term according to the row and column indices to the transpose of the pure deformation strain term, perform a quadratic product operation on the pure deformation strain term, the plastic reduced stiffness matrix, and the transpose of the pure deformation strain term according to the same row and column indices, extract the spatial integral weight corresponding to each beam element in the dynamic collision calculation domain, and accumulate the quadratic product operation results item by item according to the spatial integral weights to obtain the local deformation dissipation energy.

8. The collision simulation method for steel column hoisting based on a physics engine according to claim 2, characterized in that, The steps for obtaining the collision contact force vector are as follows: Read the beam element number, yield position index, and spatial integral weight corresponding to the local deformation dissipation energy. Match the preset initial contact stiffness coefficient according to the beam element number. Convert the local deformation dissipation energy into a damage degradation factor. Use the damage degradation factor to reduce the preset initial contact stiffness coefficient to obtain an equivalent contact stiffness coefficient. Extract the velocity vector of the steel column and the velocity vector of the scaffold rigid body node group at the initial collision contact point coordinates. Calculate the difference between the velocity vector of the steel column and the velocity vector of the scaffold rigid body node group to obtain the relative motion velocity. Combine the geometric penetration amount, relative motion velocity, equivalent contact stiffness coefficient, and preset contact damping coefficient to calculate the collision contact force amplitude. Expand the collision contact force amplitude along the surface contact normal vector direction to generate the collision contact force vector.

9. The collision simulation method for steel column hoisting based on a physics engine according to claim 2, characterized in that, The steps for obtaining the collision response state of the steel column are as follows: Read the node index of the local upgraded node group, the locking index of the boundary constant, and the time step of the current calculation frame in the dynamic collision calculation domain. Write the collision contact force vector into the external excitation term according to the node index corresponding to the initial collision contact point coordinates. Substitute the external excitation term into the dynamic equilibrium equation of the dynamic collision calculation domain. Solve the node displacement change of the local upgraded node group item by item according to the time step of the current calculation frame to obtain the node displacement increment. Superimpose the node displacement increment on the initial spatial coordinates of the rigid body node group of the scaffold according to the same node index to generate the scaffold damaged deformation coordinates. Read the spatial displacement parameters of the steel column in the current calculation frame, write the damaged deformation coordinates of the scaffolding into the rendering parameter register according to the node index of the scaffolding rigid body node group, write the spatial displacement parameters of the steel column in the current calculation frame into the rendering parameter register according to the steel column component index, check the writing status of the node index of the scaffolding rigid body node group and the steel column component index, and issue a status change command when the writing status is completed, and synchronously update the deformation display status corresponding to the damaged deformation coordinates of the scaffolding and the displacement display status corresponding to the spatial displacement parameters of the steel column in the current calculation frame to obtain the collision response status of the steel column.

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