Simulation calculation method, device, medium and equipment for thin-shell transient jump behavior
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- DALIAN UNIV OF TECH
- Filing Date
- 2025-09-19
- Publication Date
- 2026-06-26
Smart Images
Figure CN121279005B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of computational solid mechanics and structural dynamics, and in particular to a simulation calculation method, apparatus, medium and device for the transient jump behavior of thin shells. Background Technology
[0002] Thin-shell structures are space-based thin-walled systems with a curved mid-surface, a thickness much smaller than the radius of curvature and planar dimensions, and a core load-bearing mechanism based on the coupling of membrane stress and bending stress under the Kirchhoff-Leff assumption. Thin-shell structures can switch between multiple stable configurations through large elastic deformation; their abrupt changes originate from discontinuous dynamic processes involving abrupt changes in strain energy barriers. These structures have crucial applications in aerospace deployable mechanisms (such as thin-film solar sails), biomimetic soft robot actuators, and energy absorption devices.
[0003] Currently, three main technical approaches are used in the analysis of thin-shell buckling: explicit dynamic algorithms, based on the central difference principle, discretize the equations of motion and control computational stability through critical time steps to directly solve for the transient response; implicit iterative improvement methods introduce artificial damping terms to optimize the convergence of Newton's iterations and combine incremental load control strategies to track the structural equilibrium path; and reduced-order model techniques construct nonlinear subspaces through eigenorthogonal decomposition, compressing the system's degrees of freedom to 5%-10% of their original size for rapid solutions. These three methods address thin-shell buckling analysis from three dimensions: transient solution, static path tracing, and model simplification. Explicit methods focus on capturing inertial effects, implicit methods focus on post-buckling path continuity, and reduced-order models aim to improve computational efficiency.
[0004] However, while explicit dynamic algorithms can directly capture transient responses, they are constrained by the rigid constraints of the Courant-Friedrichs-Lewy condition on the critical time step. During the thin-shell transition phase, the step size is forced to be compressed to the microsecond level, resulting in exponential consumption of computational resources. Implicit iterative improvement methods, although maintaining path continuity through arc length control, mask the singularity of the Hessian matrix (det(H)→0) at the saddle point of the potential energy surface through artificial damping, generating non-physical pseudo-equilibrium solutions at bifurcation points, particularly leading to distortion of multi-stable transition paths. While order reduction model techniques significantly compress degrees of freedom, the imposed symmetry constraints inherently prevent them from describing the symmetry-breaking-dominated transition process, causing path predictions in nonlinear dynamic fields to deviate from physical reality. These three types of defects collectively constitute the technical bottleneck—the efficiency constraints of explicit methods, the path drift of implicit methods, and the physical distortion of order reduction methods—ultimately hindering the realization of high-precision analysis of thin-shell dynamic transitions. Summary of the Invention
[0005] Based on this, it is necessary to propose an efficient simulation calculation method, device, medium and equipment for the transient jump behavior of thin shells to address the above problems, and solve the two technical bottlenecks in the existing technology: inaccurate jump path prediction and explicit step size lock-up.
[0006] A simulation calculation method for the transient jump behavior of a thin shell, the method comprising the following steps:
[0007] S1: Establish a thin shell finite element analysis model, which includes a geometric model, a thin shell large deformation constitutive model, dynamic equilibrium equations, and a discretized model;
[0008] S2: Based on the aforementioned thin-shell finite element analysis model, perform time-series simulation analysis of the transient jump behavior of the thin-shell, including the following steps in each time step:
[0009] S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element.
[0010] S22: Based on the nonlinear criterion index and the local stiffness spectrum radius of each unit, the solution domain is divided into units. When the nonlinear criterion index of a unit is greater than a preset nonlinear threshold and the local stiffness spectrum radius is greater than a preset critical softening threshold, the unit is divided into an explicit domain unit; otherwise, it is divided into an implicit domain unit.
[0011] S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used.
[0012] S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21.
[0013] S25: Construct a deformation trial displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation trial displacement vector in the next time step, then proceed to step S21.
[0014] A simulation computing device for the transient jump behavior of a thin shell, comprising:
[0015] The model building module is used to build a thin shell finite element analysis model, which includes a geometric model, a thin shell large deformation constitutive model, dynamic equilibrium equations, and a discretized model.
[0016] The simulation analysis module is used to perform time-series simulation analysis of the transient jump behavior of the thin shell based on the thin shell finite element analysis model. Each time step includes the following steps:
[0017] S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element.
[0018] S22: Based on the nonlinear criterion index and the local stiffness spectrum radius of each unit, the solution domain is divided into units. When the nonlinear criterion index of a unit is greater than a preset nonlinear threshold and the local stiffness spectrum radius is greater than a preset critical softening threshold, the unit is divided into an explicit domain unit; otherwise, it is divided into an implicit domain unit.
[0019] S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used.
[0020] S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21.
[0021] S25: Construct a deformation trial displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation trial displacement vector in the next time step, then proceed to step S21.
[0022] A computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the simulation calculation method for the transient jump behavior of the thin shell described above.
[0023] A computer device includes a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the following steps:
[0024] S1: Establish a thin shell finite element analysis model, which includes a geometric model, a thin shell large deformation constitutive model, dynamic equilibrium equations, and a discretized model;
[0025] S2: Based on the aforementioned thin-shell finite element analysis model, perform time-series simulation analysis of the transient jump behavior of the thin-shell, including the following steps in each time step:
[0026] S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element.
[0027] S22: Based on the nonlinear criterion index and the local stiffness spectrum radius of each unit, the solution domain is divided into units. When the nonlinear criterion index of a unit is greater than a preset nonlinear threshold and the local stiffness spectrum radius is greater than a preset critical softening threshold, the unit is divided into an explicit domain unit; otherwise, it is divided into an implicit domain unit.
[0028] S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used.
[0029] S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21.
[0030] S25: Construct a deformation trial displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation trial displacement vector in the next time step, then proceed to step S21.
[0031] Implementing the embodiments of the present invention will have the following beneficial effects:
[0032] This invention, through nonlinear criterion indices and local stiffness spectrum radius, and based on a real-time strain rate sensing mechanism, intelligently divides explicit and implicit domain elements. For explicit domain elements of nonlinear strain (high transient jump region), a substep control technique is adopted to dynamically adjust the time increment according to the local stiffness, thereby improving the calculation accuracy before and after transient jump behavior. For implicit domain elements of linear strain, an adaptive step size technique is adopted to achieve large step size advancement while maintaining calculation stability, thereby improving calculation efficiency.
[0033] By using the energy field change characterization function, the change in structural potential energy is calculated in each deformation step. By using the stability criterion and combining it with the finite element analysis model, the comprehensive effect of material strain energy evolution and external load work can be covered. That is, a multi-steady transition path decision mechanism based on strain energy can automatically warn whether the structure is approaching a deformation bifurcation point.
[0034] When approaching the deformation bifurcation point, the deformation trial displacement vector is constructed using the direction of the fastest decrease in potential energy function, which generates the minimum energy barrier crossing path and accurately captures the real physical path of the jump behavior under various working conditions.
[0035] The entire technical system of this invention forms a closed loop of "perception-decision-execution", which comprehensively improves the efficiency, accuracy and stability in thin-shell jump simulation. Attached Figure Description
[0036] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0037] in:
[0038] Figure 1 This is a flowchart illustrating a simulation calculation method for the transient jump behavior of a thin shell according to a specific embodiment of the present invention.
[0039] Figure 2 This is a schematic diagram of the spatial position vector of a thin shell and the neutral surface.
[0040] Figure 3 It is the parameter domain, reference configuration, and deformation configuration diagram of the neutral surface of the thin shell.
[0041] Figure 4 It is a graph showing the relationship between the energy and deformation state of a thin shell (potential energy curve).
[0042] Figure 5 This is a flowchart of an explicit / implicit domain unit partitioning method according to a specific embodiment of the present invention.
[0043] Figure 6 This is a structural block diagram of a computer device according to a specific embodiment of the present invention. Detailed Implementation
[0044] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0045] refer to Figure 1 This invention provides a simulation calculation method for the transient jump behavior of a thin shell, comprising the following steps:
[0046] S1: Establish a finite element analysis model for the thin shell, including the geometric model, the constitutive model of the thin shell with large deformation, the dynamic equilibrium equations, and the discretized model.
[0047] In step S1 above, specifically, in one embodiment, after the geometric model completes the thin-shell structure design in commercial CAD software, the surface geometry information (IGES / STEP format) is exported to establish the surface geometry of the thin-shell, such as... Figure 2 As shown.
[0048] In one specific embodiment, reference is made to Figure 3 The discretized model uses a four-node hybrid interpolation tensor component unit. Each four-node hybrid interpolation tensor component unit contains four nodes, and each node includes three translational displacement components. u , v , w ) and 2 normal rotation angles ( θx , θy The displacement field is:
[0049]
[0050] In the formula ζ ∈[ [1,1] represents the natural coordinates in the thickness direction. For bilinear functions:
[0051]
[0052] These are the natural coordinates (or isoparametric coordinates) of the nodes on the surface of the element, and their values range from [ 1,1], It is the coordinate value of the i-th node in the natural coordinate system, and the thickness of the shell is denoted as . .
[0053] To eliminate shear lock-in, an assumed shear strain field is introduced. Using the MITC method, the assumed shear strain field is:
[0054]
[0055] Where A, B, C, and D are the midpoints of the element boundary. The assumed shear strain at the midpoint of the element edge of the four-node hybrid interpolation tensor component element is given.
[0056] Green-Lagrange strain tensor components Defined in the local curvilinear coordinate system (ξ,η,ζ) as:
[0057]
[0058] in, The tensor components are used to measure the initial configuration. Measure the tensor components for the current configuration. These represent the coordinate directions corresponding to the row and column of the strain tensor, respectively. ξ is the component index of the local curvilinear coordinate system (ξ,η,ζ).
[0059] We obtain the following by transforming the displacement gradient tensor using the chain rule:
[0060]
[0061] in, It represents the deformation gradient tensor from the current configuration to the reference configuration, describing the rate of change of displacement of a material point. Represents the current configuration position vector (coordinates after deformation). Represents the reference configuration position vector (coordinates before deformation). This is the inverse matrix of the reference configuration basis vectors.
[0062] The specific component calculations employ the local basis vector method, in the current configuration. The formula for calculating the direction basis vector is:
[0063] ,
[0064] In thin-shell theory, the Green-Lagrange strain tensor It can be linearly decomposed into membrane strain (in-plane strain) on the mid-surface. and bending strain (curvature change) Two parts:
[0065]
[0066] Its components are respectively
[0067]
[0068]
[0069] in, The in-plane basis vector for the current / reference configuration, subscript , where is the coordinate within the shell. This is the partial derivative of the normal vector for the current / reference configuration.
[0070] In establishing a thin-shell finite element model, accurate characterization of material constitutive relations is crucial for ensuring the accuracy of large deformation behavior analysis. This invention employs a widely applicable large deformation constitutive framework, using the principles of continuum mechanics to construct a mathematical projection relationship between the three-dimensional material model and the two-dimensional state of the thin shell.
[0071] Derivation of plane stress state constraint conditions using Kirchhoff's assumption:
[0072]
[0073] in, This indicates that the stress in the thickness direction (3 directions) is zero.
[0074] This condition serves as a bridge for converting from a three-dimensional constitutive model to a two-dimensional thin-shell model, in order to solve for the numerical rate of change:
[0075]
[0076] in, Let be the strain energy density function. , is a Jacobian determinant. Elongation ratio (the ratio of the length after deformation to the original length).
[0077] This equation needs to be solved using the Newton-Raphson method in each iteration. The numerical solution process is as follows:
[0078]
[0079] in, This represents the number of iterations.
[0080] The equation is updated in each iteration until the residual is less than the allowable value. The two-dimensional strain energy function is then reconstructed in a co-rotating local coordinate system.
[0081]
[0082] Based on this, the tangent modulus tensor components of the plane stress state are calculated. First, the basis vectors are established and the Green's strain tensor is projected onto the local system:
[0083]
[0084] in, For the global Green's strain tensor, , Let be the basis vectors of the local coordinate system. The above equation transforms the global Green strain tensor to the local system.
[0085] Based on two-dimensional reduced strain energy function Calculate the tangent modulus components under plane stress:
[0086]
[0087] Among them, subscript This represents the index of the fourth-order tensor components.
[0088] Stored in Voigt notation as a 3×3 matrix:
[0089]
[0090] By incorporating the shear strain correction of the MITC4 element and introducing a shear strain energy function correction term, the tangent modulus tensor in the large deformation constitutive model of the thin shell is obtained as follows:
[0091]
[0092] Among them, shear modulus G Derived from constitutive parameters, The assumed shear strain of MITC4 at the midpoint of the element edge.
[0093] Five Gaussian integration points along the thickness direction (integration locations) Gaussian point weights Numerical integration is performed to calculate the total stiffness matrix of the element. :
[0094] in, This is the local coordinate system transformation matrix at the integration point. Let be the stiffness matrix at the k-th Gaussian integration point. The Gaussian point weights are used.
[0095] The above-mentioned modeling system provides a unified theoretical basis for the analysis of large deformation of thin shells.
[0096] In the above scheme, the present invention introduces a strain field correction method, collects strain data at key points of the element boundary, and independently constructs a shear field through a special interpolation function to ensure numerical stability under large deformation, thereby eliminating the shear locking problem common in traditional elements.
[0097] Under dynamic loads, the dynamic equilibrium equations based on MITC4 shell elements need to accurately characterize large deformations, rotational inertia, and material nonlinear effects. The following establishes a complete equation system based on the principle of virtual work and the characteristics of MITC4. In a specific embodiment, the dynamic equilibrium is expressed as follows:
[0098]
[0099] in, Internal energy is a form of empty skill. It is inertial force virtual work. The damping force is virtual work. It is an external effort that is ultimately ineffective. This is a virtual displacement.
[0100] Within the updated Lagrange framework, the equation for the virtual work of dynamics is extended to:
[0101]
[0102] in, The virtual work functional represents the total virtual work of the system under virtual displacement (the difference between the virtual work of internal forces and the virtual work of external forces). This represents the second type of Piola-Kirchhoff stress tensor, which describes the stress state after deformation. Represents the virtual strain tensor, and the virtual displacement. Related, For material density, Let be the acceleration vector, and be the second derivative over time. The damping coefficient is... For velocity vectors, It is volume. For surface forces on the boundary, The boundary to which surface forces are applied.
[0103] The contribution of rotational inertia is not negligible; element mass matrix Block-based computation:
[0104]
[0105] Where N t It is a translational shape function. J is a rotational shape function. a =diag( J θx , J θy ) is the moment of inertia tensor.
[0106] Element damping matrix A damping array is established using a similar method. It is composed of the unit damping matrix Combining these elements, such as a single Rayleigh damper:
[0107]
[0108] in, It is the Rayleigh damping coefficient.
[0109] Tangent stiffness matrix From the element stiffness matrix The results are obtained by combining the equations. In summary, the dynamic equilibrium equations are:
[0110]
[0111] Among them, mass array It is composed of the unit mass matrix Combined, Represents external forces. This represents internal resilience. The discretized model is obtained through the following steps:
[0112] First, the dynamic equilibrium equations are transformed into a system of algebraic equations at discrete time points using the Newmark-β time integration method, thus transforming the continuous-time problem into a discrete problem that can be solved step by step. As an implicit method, the Newmark-β method has good numerical stability when solving nonlinear problems, and is especially suitable for the analysis of systems with varying stiffness or nonlinearity.
[0113] Then, the algebraic equations discretized by the Newmark-β method are solved using iterative methods (such as the Newton-Raphson method). The iterative equations are gradually corrected through linear approximation until the equilibrium condition is met.
[0114] Specifically, displacement and velocity updates include rotational degrees of freedom:
[0115]
[0116]
[0117] in, Indicates the first Rotational displacement at the time step Indicates the first Rotational displacement at the time step This represents the rotational angular velocity at time step n. Indicates the first angular velocity of rotation at the time step The time step controls the discretization accuracy. The weighting parameters for acceleration affect the accuracy of displacement calculations. The velocity-weighted parameters affect the stability of velocity calculations. In a specific embodiment, the unconditionally stable parameters are: β =0.25, γ =0.5. Solve the incremental form equation at each time step:
[0118]
[0119] in, Indicates the first The displacement increment of the next iteration. Indicates the first Internal restoring force during the next iteration and Indicates the first Acceleration and velocity at each iteration.
[0120] In the above scheme, the material model of this invention adopts a third-order nonlinear constitutive relation, which can capture the stress-response characteristics of the entire process from elasticity to softening. The model integrates shear strain correction technology to form a complete geometry-material coupling system.
[0121] Of course, in other embodiments, other existing thin-shell large deformation constitutive models, dynamic equilibrium equations, and discretized models can also be used.
[0122] S2: Based on the thin-shell finite element analysis model, a time-series simulation analysis of the transient jump behavior of the thin-shell is performed. Each time step includes the following steps, such as... Figure 5 As shown:
[0123] S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element.
[0124] At the center point of each MITC4 element in the thin-shell structure (at natural coordinates ξ=0, η=0), the strain tensor change between two consecutive time steps is tracked in real time. This essentially reflects the material deformation rate—if an element undergoes drastic deformation (such as jump or buckling) within a very short time, its strain change will increase significantly. By calculating the strain rate eigenvalue spectrum, key physical phenomena during the deformation process can be captured. First, a local strain rate tensor calculation model is constructed:
[0125]
[0126] in, ξ c =0, η c =0 represents the natural coordinates of the cell center. In time t Time unit e The local strain rate tensor is a second-order tensor that represents the rate at which the strain at the center point of the element changes with time.
[0127] Δ t It is the time step, that is, from the time step n 1 to n The time elapsed; It is a specific integration point ( The strain-displacement matrix (also known as the geometric matrix) on the ) and They represent the first n Time step and the n The element displacement vector at time step 1.
[0128] Calculate the strain rate eigenvalue spectrum based on the local strain rate tensor. :
[0129]
[0130] in, It is a function for calculating the eigenvalues of a tensor.
[0131] The eigenvalue spectrum of the strain rate tensor can be used to analyze the dynamic deformation behavior of materials (such as plastic flow, fracture, etc.). The maximum eigenvalue ( ) reveals the deformation rate in the principal tensile direction, the minimum eigenvalue ( The eigenvalue reflects the compressive or shear deformation strength, and the sign of the eigenvalue indicates the deformation mode (positive values for tension, negative values for compression). The nonlinear strength index of the element is determined by the eigenvalue criterion. :
[0132]
[0133] in, To preset a nonlinear threshold, denoted as the critical strain rate of the material.
[0134] when That is, when the absolute value of any feature exceeds a preset threshold This indicates that the unit region is in a state of strong nonlinear deformation. This includes geometric nonlinearity, such as large rotation / large curvature deformation (wrinkle formation), and material nonlinearity, such as the critical stage of stiffness degradation in hyperelastic materials.
[0135] Local stiffness spectrum radius The method for calculating the radius of the local stiffness spectrum, which reflects the degree of softening of a material, is as follows:
[0136]
[0137] in, For unit e In the tangent stiffness matrix of the current iteration step, Indicates calculation The eigenvalues, representing the "scaling factor" of the stiffness matrix in a specific direction, are the eigenvalues of the local stiffness spectrum radius. That is, the maximum value of all eigenvalue moduli, used to quantify the degree of local stiffness degradation of the material.
[0138] S22: Based on the nonlinearity criterion index and local stiffness spectrum radius of each element, the solution domain is divided into elements. When the nonlinearity criterion index of an element is greater than the preset nonlinearity threshold and the local stiffness spectrum radius is greater than the preset critical softening threshold, the element is divided into an explicit domain element; otherwise, it is divided into an implicit domain element.
[0139] When the cell center point is detected η e > η thWhen the maximum eigenvalue exceeds the critical threshold, the system marks it as a strongly nonlinear element; simultaneously, it verifies the local stiffness spectrum radius, only classifying it as a strongly nonlinear element when the stiffness value is higher than the material's critical softening threshold. ρ min When the condition is met, the unit is formally assigned to the explicit domain; otherwise, it is assigned to the implicit domain.
[0140] S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used.
[0141] For explicit domain elements, the dynamic equations are solved in real time using the non-iterative characteristic of the central difference method:
[0142]
[0143] in, The element stiffness matrix, for acceleration, for The displacement of the time step.
[0144] The central difference method described above directly calculates the acceleration at the next time step, updating displacement and velocity without iteration, making it suitable for transient dynamics problems.
[0145] Sub-step length for and The time step size between time steps, which is a function of the radius of the local stiffness spectrum:
[0146]
[0147] in, It is a constant that reflects the material properties and stability requirements.
[0148] The substep size is a function of the radius of the local stiffness spectrum; when the element has high local stiffness ( Smaller substeps are needed to avoid numerical oscillations, especially when element stiffness is reduced due to plastic deformation or contact. (Increase the substep size). The substep size can be increased automatically to improve computational efficiency.
[0149] The explicit substepping technique dynamically adjusts the calculation step size by adjusting the radius of the local stiffness spectrum, ensuring the stability of high-stiffness elements while optimizing the efficiency of low-stiffness regions.
[0150] The implicit domain employs the Newmark-β unconditionally stable algorithm combined with adaptive step size technique to improve solution efficiency.
[0151] Implicit domains are solved using iterative equilibrium equations. The step size adjustment depends on convergence rather than local stiffness, allowing for larger step sizes and making them suitable for rigid systems.
[0152] In this step, the essence of dynamic partitioning is to balance efficiency, accuracy, and stability in thin-shell transition analysis by precisely adapting the physical characteristics and algorithmic advantages of different regions.
[0153] S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21.
[0154] The incremental potential energy function is:
[0155]
[0156] in Let be the strain energy density function. Δu is the displacement gradient increment. Let Δu be the current strain and Δu be the displacement increment. Let be the strain energy density function after deformation. The strain energy density function is the strain energy density function when the material is undeformed. For external load vector, This indicates that work is done by an external force. For volume, It is a thin-shell configuration in the integration domain;
[0157] The geometric properties of the potential field are characterized by the Hessian matrix:
[0158]
[0159] in, The continuous tangent modulus matrix of the material depends on the material constitutive model used. This is the strain-displacement matrix.
[0160] Next, the bifurcation points are detected in real time, and the minimum eigenvalue λ of the Hessian matrix is calculated. min Using stability criteria, determine whether the system is about to enter a bifurcation point:
[0161]
[0162] in, It is the largest eigenvalue of the initial linear elastic stiffness matrix of the system.
[0163] S25: Construct the deformation test displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation test displacement vector in the next time step, then proceed to step S21.
[0164] If the conditions are met, the minimum eigenvector can be used. Experimental path:
[0165]
[0166] in, This is the displacement vector for this time step. It is the smallest eigenvector. To test the step size, Scaling factor For strain energy, This is the incremental potential energy gradient norm. Its physical meaning is that the system's potential energy decreases most rapidly along the direction of the fastest decrease (…). Crossing the saddle point, coefficient β Ensure that the magnitude of the displacement is proportional to the height of the potential barrier.
[0167] refer to Figure 4 (a) is a curve showing the energy change of a simple elastic thin shell as a function of its shape. Near the point of deformation, the system's energy undergoes a rapid conversion (potential energy to kinetic energy), causing it to enter a transient state and transition to a new steady state. (See reference) Figure 4 (b) illustrates a more complex energy curve for a multistable thin-shell system, containing multiple stationary points, each corresponding to a steady state, with varying transition barriers, making the transitions between steady states more complex. A potential barrier is the maximum energy difference that the energy functional must overcome to transition from one local minimum to another, reflecting the energy resistance to state transitions. A high barrier requires a large amount of external energy to change the system's state; a low barrier allows even small disturbances to trigger state changes.
[0168] Step S2 above uses nonlinear criteria and local stiffness spectrum radius, based on a real-time strain rate sensing mechanism, to intelligently divide explicit and implicit domain elements. For explicit domain elements of nonlinear strain (high transient jump region), substep control technology is used to dynamically adjust the time increment according to local stiffness, thereby improving the calculation accuracy before and after transient jump behavior. For implicit domain elements of linear strain, adaptive step size technology is used to achieve large step size advancement while maintaining calculation stability, thereby improving calculation efficiency.
[0169] By using the energy field change characterization function, the change in structural potential energy is calculated in each deformation step. By using the stability criterion and combining it with the finite element analysis model, the comprehensive effect of material strain energy evolution and external load work can be covered. That is, a multi-steady transition path decision mechanism based on strain energy can automatically warn whether the structure is approaching a deformation bifurcation point.
[0170] When approaching the deformation bifurcation point, the deformation trial displacement vector is constructed using the direction of the fastest decrease in potential energy function, which generates the minimum energy barrier crossing path and accurately captures the real physical path of the jump behavior under various working conditions.
[0171] The entire technical system of this invention forms a closed loop of "perception-decision-execution", which comprehensively improves the efficiency, accuracy and stability in thin-shell jump simulation.
[0172] In the specific embodiments described above, by solving the second derivative matrix of the potential energy surface in real time, the curvature change characteristics of the energy field can be accurately captured, and its minimum eigenvalue becomes the core indicator of stability. When the minimum eigenvalue of the curvature matrix is detected to exceed the stability threshold, the system automatically issues a warning that the structure is approaching a bifurcation point. At this time, the intelligent decision-making module is activated, generating a tentative displacement path along the potential energy decrease direction indicated by the minimum eigenvector.
[0173] This invention also discloses a simulation computing device for the transient jump behavior of thin shells, comprising:
[0174] The model building module is used to build a thin shell finite element analysis model, which includes a geometric model, a thin shell large deformation constitutive model, dynamic equilibrium equations, and a discretized model.
[0175] The simulation analysis module is used to perform time-series simulation analysis of the transient jump behavior of thin shells based on the thin shell finite element analysis model. Each time step includes the following steps:
[0176] S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element.
[0177] S22: Based on the nonlinearity criterion index and local stiffness spectrum radius of each element, the solution domain is divided into elements. When the nonlinearity criterion index of an element is greater than the preset nonlinearity threshold and the local stiffness spectrum radius is greater than the preset critical softening threshold, the element is divided into an explicit domain element; otherwise, it is divided into an implicit domain element.
[0178] S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used.
[0179] S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21.
[0180] S25: Construct the deformation test displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation test displacement vector in the next time step, then proceed to step S21.
[0181] The implementation methods of the above modules are the same as the efficient simulation calculation method for the transient jump behavior of thin shells in this invention, which has been described in detail above and will not be repeated here.
[0182] The present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform a simulation calculation method for the transient jump behavior of a thin shell as described above, the method comprising the following steps:
[0183] S1: Establish a thin shell finite element analysis model, which includes a geometric model, a thin shell large deformation constitutive model, dynamic equilibrium equations, and a discretized model;
[0184] S2: Based on the aforementioned thin-shell finite element analysis model, perform time-series simulation analysis of the transient jump behavior of the thin-shell, including the following steps in each time step:
[0185] S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element.
[0186] S22: Based on the nonlinear criterion index and the local stiffness spectrum radius of each unit, the solution domain is divided into units. When the nonlinear criterion index of a unit is greater than a preset nonlinear threshold and the local stiffness spectrum radius is greater than a preset critical softening threshold, the unit is divided into an explicit domain unit; otherwise, it is divided into an implicit domain unit.
[0187] S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used.
[0188] S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21.
[0189] S25: Construct a deformation trial displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation trial displacement vector in the next time step, then proceed to step S21.
[0190] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.
[0191] The present invention also discloses a computer device, including a memory and a processor. The memory stores a computer program, and when the computer program is executed by the processor, the processor performs a simulation calculation method for the transient jump behavior of a thin shell as described above. The method includes the following processes:
[0192] S1: Establish a thin shell finite element analysis model, which includes a geometric model, a thin shell large deformation constitutive model, dynamic equilibrium equations, and a discretized model;
[0193] S2: Based on the aforementioned thin-shell finite element analysis model, perform time-series simulation analysis of the transient jump behavior of the thin-shell, including the following steps in each time step:
[0194] S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element.
[0195] S22: Based on the nonlinear criterion index and the local stiffness spectrum radius of each unit, the solution domain is divided into units. When the nonlinear criterion index of a unit is greater than a preset nonlinear threshold and the local stiffness spectrum radius is greater than a preset critical softening threshold, the unit is divided into an explicit domain unit; otherwise, it is divided into an implicit domain unit.
[0196] S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used.
[0197] S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21.
[0198] S25: Construct a deformation trial displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation trial displacement vector in the next time step, then proceed to step S21.
[0199] Figure 6 An internal structural diagram of a computer device in one embodiment is shown. This computer device can specifically be a terminal or a server. Figure 6 As shown, the computer device includes a processor, memory, and network interface connected via a system bus. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system and may also store a computer program. When executed by the processor, this computer program enables the processor to implement a simulation calculation method for the transient behavior of a thin-shell structure. The internal memory may also store a computer program, which, when executed by the processor, enables the processor to implement a simulation calculation method for the transient behavior of a thin-shell structure. Those skilled in the art will understand that... Figure 6 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.
[0200] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0201] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of this patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims. Please enter the specific implementation details.
Claims
1. A simulation calculation method for the transient jump behavior of a thin shell, characterized in that, The process includes the following: S1: Establish a thin shell finite element analysis model, which includes a geometric model, a thin shell large deformation constitutive model, dynamic equilibrium equations, and a discretized model; S2: Based on the aforementioned thin-shell finite element analysis model, perform time-series simulation analysis of the transient jump behavior of the thin-shell, including the following steps in each time step: S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element. S22: Based on the nonlinear criterion index and the local stiffness spectrum radius of each unit, the solution domain is divided into units. When the nonlinear criterion index of a unit is greater than a preset nonlinear threshold and the local stiffness spectrum radius is greater than a preset critical softening threshold, the unit is divided into an explicit domain unit; otherwise, it is divided into an implicit domain unit. S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used. S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21. S25: Construct a deformation trial displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation trial displacement vector in the next time step, then proceed to step S21; In steps S21 and S22, the local strain rate tensor is: in ξ c =0, η c =0 represents the natural coordinates of the cell center; In time t Time unit e The local strain rate tensor; Δ t It is the time step; It is a specific integration point ( The strain-displacement matrix on the surface; and They represent the first n Time step and the n The element displacement vector at time step 1; The strain rate characteristic spectrum is: in It is a function for calculating the eigenvalues of a tensor; The nonlinear strength index is: The preset nonlinear threshold , The critical strain rate of the material; and These are the maximum and minimum eigenvalues extracted from the eigenvalue spectrum; The formula for calculating the radius of the local stiffness spectrum is: in, For unit e In the tangent stiffness matrix of the current iteration step, Indicates calculation eigenvalues.
2. The simulation calculation method for the transient jump behavior of thin shells according to claim 1, characterized in that, The discretization model employs a four-node hybrid interpolation tensor component unit, which contains four nodes, each of which includes three translational displacement components. u , v , w ) and 2 normal rotation angles ( θx , θy The displacement field is: In the formula ζ ∈[ [1,1] represents the natural coordinates in the thickness direction. It is a bilinear function. in, These are the natural coordinates of the nodes on the surface within the element. It is the coordinate value of the i-th node in the natural coordinate system, and the thickness of the shell is denoted as . .
3. The simulation calculation method for the transient jump behavior of thin shells according to claim 1, characterized in that, The tangent modulus tensor in the large deformation constitutive model of the thin shell is: in, The components are: The term following the plus sign is the correction term for the shear strain energy function, where the shear modulus G is derived from the constitutive parameters. For the Green-Lagrange strain tensor, The energy density function is represented by the subscript. This represents the index of a fourth-order tensor component. The assumed shear strain at the midpoint of the element edge for a four-node hybrid interpolation tensor component element; Where A, B, C, and D are the midpoints of the element boundary; The total stiffness matrix of the element can be obtained by performing Gaussian integration along the thickness direction. : For the transformation matrix, Let be the stiffness matrix at the k-th Gaussian integration point. The Gaussian point weights are used.
4. The simulation calculation method for the transient jump behavior of thin shells according to claim 1, characterized in that, The dynamic equilibrium equation is: in, For mass array, It is displacement. It is the displacement increment. It is a velocity vector. It is an acceleration vector. It is an external force. It is internal resilience; mass array It is composed of the unit mass matrix Combining the results, we get: in, It is the volume of a unit domain. It is the material density, N t It is a translational shape function. J is a rotational shape function. a =diag( J θx , J θy () represents the moment of inertia tensor. It is volume; Damping array It is composed of the unit damping matrix Combining the results, we get: in, It is the Rayleigh damping coefficient; Tangent stiffness matrix From the element stiffness matrix The combination yields the result.
5. The simulation calculation method for the transient jump behavior of thin shells according to claim 1, characterized in that, In step S24, the energy field change characterization function adopts the incremental potential energy function: in Let be the strain energy density function. Δu is the displacement gradient increment. For displacement increment, In response to the current situation, For volume; The stability criterion is: in It is the smallest eigenvalue of the Hessian matrix. It is the largest eigenvalue of the system's initial linear elastic stiffness matrix; The expression for the Hessian matrix is: in The continuous tangent modulus matrix of the material depends on the material constitutive model used. This is the strain-displacement matrix.
6. The simulation calculation method for the transient jump behavior of thin shells according to claim 1, characterized in that, In step S25, the deformation probe displacement vector is: in This is the displacement vector for this time step. It is the smallest eigenvector. To test the step size, Scaling factor For strain energy, Let be the incremental potential energy gradient norm.
7. A simulation computing device for the transient jump behavior of a thin shell, characterized in that, include: The model building module is used to build a thin shell finite element analysis model, which includes a geometric model, a thin shell large deformation constitutive model, dynamic equilibrium equations, and a discretized model. The simulation analysis module is used to perform time-series simulation analysis of the transient jump behavior of the thin shell based on the thin shell finite element analysis model. Each time step includes the following steps: S21: Calculate the local strain rate tensor at the center point of each element in the current time step and the previous time step, obtain the strain rate eigenvalue spectrum, and then obtain the nonlinear strength index and local stiffness spectrum radius of each element. S22: Based on the nonlinear criterion index and the local stiffness spectrum radius of each unit, the solution domain is divided into units. When the nonlinear criterion index of a unit is greater than a preset nonlinear threshold and the local stiffness spectrum radius is greater than a preset critical softening threshold, the unit is divided into an explicit domain unit; otherwise, it is divided into an implicit domain unit. S23: For explicit domain elements, a substep control technique is used, where the substep size is a function of the local stiffness spectrum radius; for implicit domain elements, an adaptive step size technique is used. S24: Based on the deformed thin shell configuration, calculate the incremental potential energy function between the current time step and the previous time step, obtain the energy field change characterization function, and use the stability criterion to determine whether the thin shell is about to enter the deformation bifurcation point. If so, proceed to step S25; otherwise, proceed to step S21. S25: Construct a deformation trial displacement vector using the direction of the fastest decrease in the potential energy function, and continue the calculation based on the deformation trial displacement vector in the next time step, then proceed to step S21; In steps S21 and S22, the local strain rate tensor is: in ξ c =0, η c =0 represents the natural coordinates of the cell center; In time t Time unit e The local strain rate tensor; Δ t It is the time step; It is a specific integration point ( The strain-displacement matrix on the surface; and They represent the first n Time step and the n The element displacement vector at time step 1; The strain rate characteristic spectrum is: in It is a function for calculating the eigenvalues of a tensor; The nonlinear strength index is: The preset nonlinear threshold , The critical strain rate of the material; and These are the maximum and minimum eigenvalues extracted from the eigenvalue spectrum; The formula for calculating the radius of the local stiffness spectrum is: in, For unit e In the tangent stiffness matrix of the current iteration step, Indicates calculation eigenvalues.
8. A computer-readable storage medium storing a computer program that, when executed by a processor, causes the processor to perform the steps of the method as claimed in any one of claims 1 to 6.
9. A computer device comprising a memory and a processor, the memory storing a computer program that, when executed by the processor, causes the processor to perform the steps of the method as claimed in any one of claims 1 to 6.