Dynamic analysis method for coupling of particle system and membrane structure

Abstract

The invention discloses a dynamic analysis method for coupling of a particle system and a membrane structure, which belongs to the technical field of mechanical analysis and comprises the following steps: (1) representing particle motion by particle mass center motion; the membrane structure is divided into membrane units, the junction points between the membrane units are membrane unit mass points, and the coupling effect of the particle system and the membrane structure is simulated through a contact unit; (2) dividing the responsible range of the membrane units, calculating the contact force between the particles and the membrane units to which the particles belong, applying the contact force to the mass centers of the particles, and distributing the contact force through a weighting coefficient and reversely applying the contact force to the mass points of the membrane units; (3) calculating the contact force among particles in the particle system, and applying the contact force to the mass center of the particles; integrating all acting forces on particle mass points to judge the particle motion condition; and (4) analyzing the membrane structure by adopting a finite mass point method, calculating the internal force of the membrane unit to obtain the mass point internal force of the membrane unit, and integrating the mass point acting force of the membrane unit to judge the movement condition of the mass points of the membrane unit so as to obtain the displacement and deformation conditions of the membrane structure.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical analysis, and in particular relates to a dynamic analysis method for coupling a particle system with a membrane structure. Background Art

[0002] Membrane structure is a representative of flexible space structure. It deforms greatly under external loads and is prone to bag effect, causing structural damage. The accumulation of particles such as snow, sand, and hail is an important influencing factor in the use analysis of membrane structures. The membrane structure and the above-mentioned particle system affect each other, and the coupling effect between the two cannot be ignored. Taking sand as an example, sand particles accumulate on the membrane surface, and their distribution on the membrane surface affects the mechanical properties of the structure. When the membrane structure is subjected to the load generated by the accumulated sand particles, it will be locally concave, which in turn affects the distribution of sand particles. This repetitive process is likely to cause the bag effect of the membrane structure. Therefore, it is necessary to study the coupling effect between membrane structure and particle systems such as snow, sand, and hail.

[0003] The coupling between particle systems and membrane structures has a great influence on the design and use of membrane structures. However, since it involves the coupling between large-scale particle motion and structures prone to large deformation, there is still a lack of research in the relevant dynamic analysis. Therefore, the dynamic analysis method of the coupling between particle systems and membrane structures is urgently needed to be supplemented and improved in current scientific research and engineering applications, and the contact search between particles and membrane structures is the basis for completing the coupling analysis.

[0004] In the prior art, the dynamic analysis methods for the coupling of particle systems and membrane structures often have the following defects:

[0005] 1) At present, the coupling analysis methods of particle systems and membrane structures are mostly based on the background of fluid-solid coupling analysis of wind and membrane structures. The influencing factors of particles such as snow are added when setting fluid parameters. There is a lack of dynamic analysis methods that directly consider the coupling effect between particles and membrane structures.

[0006] 2) Current point-to-surface contact research methods mostly use projection methods (such as Chinese patent document CN104573269A, etc.). However, when the membrane structure is prone to large deformation and large angles are easily generated between membrane units, point-to-surface contact judgment is prone to over-judgment and missed judgment, resulting in unrealistic rebound of particles or penetration of the membrane structure.

[0007] 3) At present, most membrane structure analysis methods use the finite element method based on the theory of continuum mechanics, and the finite element method needs to integrate the overall stiffness matrix (such as Chinese patent document CN117373575A, etc.). This is more cumbersome when analyzing large deformation problems of membrane structures, and it is more difficult to solve after considering nonlinear factors.

[0008] In summary, the existing dynamic analysis methods for the coupling of particle systems and membrane structures have problems such as lack of analysis methods, defects in point-to-surface contact judgment methods, complex calculations, and large amount of calculations. Summary of the invention

[0009] In view of the shortcomings in the prior art, the present invention provides a dynamic analysis method for the coupling of a particle system and a membrane structure. Through effective modeling and precise analysis, especially the point-surface contact method of dividing the responsible range, the discrete element method is used to analyze the particle system and the finite particle method is used to analyze the membrane structure. This can more clearly reflect the coupling effect between the particle system and the membrane structure, and provide support for the design and use of the membrane structure under the influence of the particle environment.

[0010] The specific technical solutions adopted are as follows:

[0011] A dynamic analysis method for coupling a particle system with a membrane structure comprises the following steps:

[0012] (1) The particle motion is represented by the particle center motion, and the particles are simulated by discrete units; the membrane structure is divided into several independent membrane units, and the intersection points between the membrane units are the membrane unit mass points (the membrane structure is discretized into mass points); the coupling between the particle system and the membrane structure is simulated by the contact unit, which is a non-solid unit that coincides with the membrane unit and is used for contact judgment and contact force calculation between the particle and the membrane unit;

[0013] (2) Preliminarily screen the potential contact particles of each membrane unit through global search, determine the global coordinates of the potential contact particles, divide the responsible range of the membrane unit, calculate the local coordinates of the potential contact particles within the responsible range of the membrane unit, determine the membrane unit to which the particle belongs based on the local coordinates and judge the actual contact relationship between the particle and the membrane unit to which it belongs, calculate the contact force between the particle and the membrane unit to which it belongs, apply the contact force to the particle's center of mass, and distribute the contact force through the weighted coefficient and reversely apply it to the membrane unit mass point;

[0014] (3) calculating the contact force between particles in the particle system and applying the contact force to the particle mass center; judging the movement of the particle mass center according to the mass of the particle, the external force on the particle, the contact force between the particle and the membrane unit to which it belongs in step (2), and the damping force; the movement of the particle mass center represents the movement of the particle;

[0015] (4) The membrane structure is analyzed by the finite particle method, and the internal force of the membrane unit is calculated to obtain the internal force of the membrane unit particle. The movement of the membrane unit particle is determined based on the mass distributed to the membrane unit particle, the external force of the membrane unit particle, the internal force of the membrane unit particle, the contact force with a weighted coefficient in step (2), and the damping force. Further, the displacement and deformation of the membrane structure are obtained based on the movement of the membrane unit particle.

[0016] Preferably, the membrane plane is divided into triangular plane units by grids and oblique lines, and the triangular plane units are used as membrane units, and the three vertices of the triangular plane units are used as membrane unit mass points.

[0017] Preferably, in step (2), the space is evenly divided into a plurality of cells, and the particles therein are indexed, and the cells within the coverage range of the target membrane unit and a certain range around it are retrieved to obtain the serial numbers of potential contact particles that may come into contact with the target membrane unit as potential contact particles.

[0018] Preferably, in step (2), the division method of the membrane unit responsible range is: based on the membrane unit mass points i, j, k, respectively calculate the average vector n of the membrane unit normal vector connected to the membrane unit mass points i, j, k i ,n j ,n k , and n i ,n j ,n k is the particle normal vector. Based on the particle, six vertices are obtained by extending the particle normal vector in the positive and reverse directions, and the six vertices are connected by straight line segments to form the responsible range of the membrane unit.

[0019] Preferably, by constructing an isoparametric unit in the range of the membrane unit, an isoparametric inverse iteration method is used to construct the forward and inverse transformation function u between the global coordinates and the local coordinates of the potential contact particles. + =∑N i (ξ,η,ζ)u i and After iterative calculation, the local coordinates (ξ,η,ζ) of the potential contact particles within the membrane unit are obtained; where the global coordinates of the potential contact particles are (x,y,z), u + is the global coordinate value of any point within the membrane unit’s range, u - is the local coordinate value of any point within the membrane unit’s range, u i is the coordinate of the membrane unit point i, N i (ξ,η,ζ) is the shape function with local coordinates (ξ,η,ζ) as independent variables, It is a shape function with global coordinates (x, y, z) as independent variables.

[0020] Furthermore, the method for determining the membrane unit to which a particle belongs is as follows: when the local coordinates (ξ, η, ζ) of the potential contact particle satisfy ξ>-1, η>-1 and ξ+η<0, the particle belongs to the scope of responsibility of the membrane unit.

[0021] Furthermore, the embedding depth of the particle on the plane of the membrane unit is calculated. When the embedding depth is greater than zero, it is determined that the particle is in contact with the membrane structure, and the contact force between the particle and the membrane unit to which it belongs is calculated. The contact force includes the point-to-surface normal contact force and the point-to-surface tangential contact force. The point-to-surface normal contact force is calculated using the penalty function method, and the point-to-surface tangential contact force is calculated using the Benson friction model.

[0022] Preferably, in step (3), the space is divided into cells, an index is established for each particle in the particle system, and particles in a 3×3×3 cell centered on the cell where the target particle is located are selected to form a potential contact particle pair with the target particle, thereby completing the preliminary screening of the potential contact particle pair. Then, by comparing the distance between the center of mass of the potential contact particle pair and the sum of the radius of the particle pair, the relative position relationship of the potential contact particle pair is obtained, the actual contact relationship between the particles is determined, the actual contact particle pair is determined, and the embedding depth of the actual contact particle pair is obtained, and the contact force between the particles is calculated.

[0023] Specifically, the particle center of mass motion is determined by the particle motion control equation, which is:

[0024]

[0025] in,

[0026]

[0027] In the formula, is the mass of the ith particle, is the mass center acceleration of the ith particle, and They represent the external force on the ith particle, the contact force between particles, the contact force between the particle and its membrane unit, and the damping force, respectively. is the mass inertia matrix of the center of mass of the ith particle, is the angular acceleration of the center of mass of the i-th particle, is the external moment of the ith particle, is the contact torque between the ith particle and other particles, is the contact torque between the ith particle and its membrane unit, is the damping moment of the ith particle, and ζ is the damping coefficient.

[0028] The membrane structure analysis method in step (4) is to deduct the rigid body translation and rotation displacement of the membrane unit by virtual inverse motion within a time step to determine the pure deformation Δu of the membrane unit within the time step. i; Establish a local coordinate system through the pure deformation vector of the membrane unit, and determine the transformation matrix T between the global coordinate system and the local coordinate system; Determine the plane stress increment of the membrane unit in the local coordinate system through the isoparametric method, stress-strain relationship and force balance relationship The internal force of the membrane unit is calculated, and the internal force of the membrane unit particle is obtained through the transformation matrix and virtual forward motion.

[0029] The displacement and deformation of the membrane structure are determined by the membrane unit mass point motion equation, which is expressed as:

[0030]

[0031] In the formula, is the mass assigned to the ith particle, is the acceleration of the ith particle, is the external force on the ith particle, is the internal force of the ith particle, is the contact force between the particle and the membrane on the ith particle, is the damping force of the ith particle.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1) The present invention proposes a dynamic analysis method for the coupling of a particle system and a membrane structure. By only considering the coupling between the particle system and the membrane structure, the coupling between the two can be more clearly reflected, providing an effective analysis method for the usage scenario where only the particle system and the membrane structure are coupled.

[0034] 2) The present invention proposes a new point-to-surface contact method for dividing the responsible range, which divides the space around the membrane structure and effectively avoids the problem of overlapping or missing responsible ranges of adjacent membrane units, that is, avoids the phenomenon of unrealistic rebound or penetration of particles through the membrane structure, and improves the existing point-to-surface contact method.

[0035] 3) The membrane structure analysis process of the present invention is based on the finite mass method, does not need to integrate the overall stiffness matrix, and the analysis of nonlinear problems is not restricted by continuity. It does not need to perform iterative solutions and special corrections when calculating displacements, which supplements the existing membrane structure modeling and dynamic analysis methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic diagram of the particle system and membrane structure model;

[0037] Figure 2 It is a schematic diagram of global search for point-surface contact;

[0038] Figure 3 It is a schematic diagram of local search for point-surface contact;

[0039] Figure 4 It is a schematic diagram of isoparametric inverse iterative solution;

[0040] Figure 5 is a schematic diagram of particle contact search;

[0041] Figure 6 It is a schematic diagram of the membrane unit calculation model;

[0042] In the figure: 1. Particle, 2. Membrane unit particle, 3. Triangular membrane unit, 4. Global search cell, 5. Particle normal vector, 6. Membrane unit responsible range, 7. Isoparametric unit, 8. Target particle. DETAILED DESCRIPTION

[0043] The present invention will be further described below in conjunction with the embodiments and accompanying drawings. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. The contents not described in detail in this specification belong to the prior art known to professionals in the field. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those of ordinary skill in the art to which this application belongs.

[0044] The present invention provides a dynamic analysis method for the coupling of a particle system and a membrane structure. The method of the present invention proposes a point-surface contact search method for dividing the responsible range; the particles are simulated by discrete units, the membrane structure is simulated by membrane units, and the coupling between the particles and the membrane plane is simulated by contact units. The coupling effect is analyzed by the point-surface contact method for dividing the responsible range, and the potential contact particles of the membrane unit are preliminarily screened by global search; the position relationship between the particle particles and the membrane unit is obtained by local search, the responsible range of the membrane unit is divided by the particle normal vector, and the relative position of the particle particles in the responsible range is calculated by the isoparametric inverse iteration method; the point-surface contact force is calculated by the contact force model. The particles are dynamically analyzed by the discrete unit method to calculate the contact force between the particles; all the forces acting on the integrated particle particles are substituted into the particle particle motion equation to solve the particle particle displacement. The membrane structure is analyzed by the finite particle method; the internal force of the membrane unit is calculated by virtual inverse motion; the integrated membrane unit particle forces are substituted into the membrane unit particle motion control equation to explicitly solve the membrane unit particle displacement. Repeat the above analysis steps to complete the dynamic analysis of the coupling of the particle system and the membrane structure.

[0045] Example

[0046] like Figure 1As shown, the particle 1 is simulated by a discrete unit, the membrane structure is simulated by a triangular membrane unit 3, and the coupling between the particle and the membrane structure is simulated by a contact unit; the discrete unit regards the particle as an independent unit, and the movement of the particle center of mass represents the movement of the particle; a number of independent membrane units are obtained by dividing a number of grid lines and oblique lines along the surface direction of the membrane structure, and the membrane structure is discretized into particles. The membrane surface is simulated by a triangular plane unit obtained by dividing the grid and the oblique lines. The triangular plane unit is composed of three membrane unit particles 2, and the plane deformation and the internal force of the membrane unit particles can be obtained by virtual inverse motion; the contact constraint between the particle and the membrane unit is simulated by the contact unit to ensure that no penetration occurs in the coupling between the particle and the membrane structure.

[0047] After the particle system and membrane structure are modeled, the motion state of the particles and membrane structure is calculated. The motion time can be divided into multiple time micro-segments. The following is the calculation method for updating the motion state of the particles and membrane structure within a time micro-segment, which is divided into three parts: coupling action calculation, particle system internal analysis and motion state update, and membrane structure internal force analysis and motion state update.

[0048] Coupling action calculation: Preliminarily screen the potential contact particles of each membrane unit through global search, determine the global coordinates of the potential contact particles, divide the responsible range of the membrane unit, calculate the local coordinates of the potential contact particles within the responsible range of the membrane unit, determine the membrane unit to which the particle belongs based on the local coordinates and judge the actual contact relationship between the particle and the membrane unit to which it belongs, calculate the contact force between the particle and the membrane unit to which it belongs, apply the contact force to the particle's center of mass, and distribute the contact force through the weighted coefficient and reversely apply it to the membrane unit mass point;

[0049] Specifically, Figure 2 As shown, the point-surface contact global search divides the space evenly into multiple global search cells 4, and indexes the particles therein, retrieves the cells within the coverage area of ​​the target membrane unit and a certain range around it, and obtains the serial numbers of potential contact particles that may come into contact with the target particles as potential contact particles.

[0050] like Figure 3 As shown in the figure, the local search of point-to-surface contact is based on the contact unit nodes (membrane unit particles) i, j, k, and calculates the average vector n of the plane unit normal vector connected to the particle. i ,n j ,n k The particle normal vector 5 is extended forward and backward on the basis of the particle, and the 6 vertices are connected by straight line segments to form the responsible range 6 of the membrane unit. The local coordinates of the particles in the responsible range are calculated by the isoparametric inverse iteration method, and the contact relationship between the particles and the membrane unit can be determined, and the point-to-surface contact force can be calculated and distributed.

[0051] like Figure 4As shown, the isoparametric inverse transformation calculates the local coordinates of the particle center of mass. First, the isoparametric unit 7 is constructed. The isoparametric unit shape function of the membrane unit is:

[0052]

[0053] The local coordinates of each node are shown in the following table:

[0054] Table 1 Local coordinates of each node of the isoparametric element

[0055]

[0056] The isoparametric inverse iteration is used to solve the local coordinates of the particle center of mass. First, a six-dimensional finite subspace is constructed:

[0057] S1=Span{1,ξ,η,ζ,ξζ,ηζ}

[0058] S2=Span{1,x,y,z,xz,yz}

[0059] Among them, S1 is the subspace related to local coordinates, S2 is the subspace related to global coordinates, and the global coordinates and local coordinates are regarded as a projection of an infinite-dimensional function in the above two subspaces. The fitting function form of the forward and inverse transformation of the isoparametric unit is as follows:

[0060] u + =ΣN i (ξ,η,ζ)u i

[0061]

[0062] In the formula, u + is the global coordinate value of any point within the membrane unit’s range, u - is the local coordinate value of any point within the membrane unit’s range, u i is the coordinate of the membrane unit point i, N i (ξ,η,ζ) is the shape function with local coordinates (ξ,η,ζ) as independent variables, It is a shape function with global coordinates (x, y, z) as independent variables, which is specifically expressed as:

[0063]

[0064] s T =[1,x,y,z,xz,yz]

[0065] c i =[c 1i ,c 2i ,…,c 6i ] T

[0066] In the formula, c i is the coefficient vector of the shape function. Then construct the matrix according to the properties of the shape function:

[0067]

[0068] The relationship between the two matrices is as follows:

[0069] C=S -1

[0070] Substituting into the calculation formula, we can get

[0071] Perform an iterative solution:

[0072] (1) Input the global coordinates of the prism nodes and the particle points to be judged Divergence threshold ε max and the iteration accuracy requirement ε;

[0073] (2) Use the global coordinate values ​​of the nodes to find the coefficient matrix C;

[0074] (3) G k Substitute the isoparametric unit inverse transformation fitting function to obtain the local coordinate approximation L k ;

[0075] (4) L k Substitute the isoparametric unit forward transformation fitting function to obtain the corresponding global coordinate G k ;

[0076] (5) If |G k -G k-1 |<ε, and k>1, the iteration stops and the output local coordinate value (ξ,η,ζ)=L k ;

[0077] (6) If |G k -G k-1 |>ε max Or if k>20, the iteration stops and the result diverges, and the particle is outside the prism;

[0078] (7) Substitute into step (3) and continue the calculation.

[0079] Next, determine whether the particle is located inside the membrane unit's responsible range. If the local coordinates are inside, the following conditions must be met:

[0080]

[0081] If the above conditions are not met, the particle point is not within the scope of the membrane unit.

[0082] If the particle meets the above conditions, we can continue to calculate the embedding depth of the particle on the plane and the direction of the normal force:

[0083]

[0084] Where, d N2S is the embedding depth, n N2S is the direction of the normal force, n i and x i are the normal vector and global coordinate of the ith node of the membrane element, n i,j is the normal vector of the jth unit plane connected to the ith node, k i is the number of units connected to the ith node, x node is the coordinate of the particle center of mass, R node is the particle radius, L i is the weighting coefficient, calculated as follows:

[0085]

[0086] When the embedding depth of the particle in the plane is greater than zero, it is determined that the particle is in contact with the membrane structure. Then the contact force model is used to calculate the contact force between the particle and the membrane structure. The contact force composition is as follows:

[0087] F N2S =F N2S,n +F N2S,s

[0088] In the formula, F N2S is the contact force between the particle and its membrane unit, F N2S,n is the point-to-surface normal contact force, F N2S,s is the point-to-surface tangential contact force, F N2S,n Using the penalty function method, F N2S,s The Benson friction model is used for calculation.

[0089] The normal contact force is calculated using the penalty function method:

[0090]

[0091] Where, d N2S is the depth of particles embedded in the membrane plane, k N2S,n is the point-to-surface normal contact stiffness, s n is the scaling factor of the point-to-surface normal contact force, V and K are the volume and bulk modulus of the membrane structure unit, respectively, and A is the area of ​​the membrane plane.

[0092] The tangential contact force F at time t N2S,s Expressed as Calculated using the Benson friction model:

[0093]

[0094]

[0095] In the formula, is the tangential force at time t, is the trial value of the tangential force at time t, k N2S,s is the tangential contact stiffness between particles, Δδ s is the tangential embedding depth increment, μ is the friction coefficient of the membrane unit surface. After the contact force between the particle and the membrane unit is calculated, the point-to-surface contact force is applied to the particle point. The contact force on the i-th particle is expressed as

[0096]

[0097] At the same time, the weighting coefficient L i The contact force is distributed and acted on the membrane unit mass point in the opposite direction. The particle-membrane contact force on the i-th membrane unit mass point is expressed as If a membrane unit particle is assigned corresponding contact forces multiple times, all contact forces calculated according to the following formula need to be accumulated;

[0098]

[0099] Internal analysis of particle system and update of motion state: calculate the contact force between particles in the particle system and apply the contact force to the particle mass center; determine the motion of the particle mass center based on the mass of the particle, the external force on the particle, the contact force between the particle, the contact force between the particle and the membrane unit to which it belongs, and the damping force;

[0100] like Figure 5 As shown in the figure, the discrete unit analysis method divides the space into cells, establishes an index for each particle in the particle system, selects particles in the 3×3×3 cells centered on the cell where the target particle 8 is located and the target particle to form potential contact particle pairs, completing the preliminary screening of potential contact particle pairs. Then, by comparing the distance between the center of mass of the potential contact particle pairs and the sum of the radius of the particle pairs, the relative position relationship of the potential contact particle pairs is obtained, the contact relationship between the particles is judged, the contact particle pairs are determined, and the embedding depth of the contact particle pairs is obtained.

[0101] The particle motion is represented by the particle center motion. By assuming that the particles are in a dynamic equilibrium state in each time iteration step during the structural motion deformation process, and any particle in the system follows Newton's second law, the particle motion control equation is:

[0102]

[0103] in,

[0104]

[0105] In the formula, is the mass of the ith particle, is the mass center acceleration of the ith particle, and They represent the external force on the ith particle, the contact force between particles, the contact force between the particle and its membrane unit, and the damping force, respectively. is the mass inertia matrix of the center of mass of the ith particle, is the angular acceleration of the center of mass of the i-th particle, is the external moment of the ith particle, is the contact torque between the ith particle and other particles, is the contact torque between the ith particle and its membrane unit, is the damping torque of the ith particle, and ζ is the damping force coefficient. By solving the motion control equation, the displacement of the particle in the time iteration step can be calculated, thereby obtaining the position and deformation of the structure at the next moment.

[0106] Internal force analysis and motion state update of membrane structure: The finite mass method is used to analyze the membrane structure, calculate the internal force of the membrane unit, and obtain the internal force of the membrane unit mass. The motion of the membrane unit mass is determined based on the mass distributed to the membrane unit mass, the external force of the membrane unit mass, the internal force of the membrane unit mass, the contact force with weighted coefficients, and the damping force. Further, the displacement and deformation of the membrane structure are obtained based on the motion of the membrane unit mass.

[0107] like Figure 6 As shown, the configuration Ω a and Ω b The membrane unit at t a Time and t b The unit configuration at the moment, the displacement vector of the particle is:

[0108]

[0109] Through the virtual reverse motion of the separable unit rigid body displacement, the pure deformation of the membrane unit is obtained. First, eliminate the rigid body translation displacement and select Ω a The midpoint is used as the reference point to transform the configuration Ω b Move parallel to make Ω b The corresponding nodes in the matrix coincide with the reference points, and the unit configuration Ω' is obtained.

[0110] Next, the out-of-plane rotation displacement of the rigid body is eliminated, and the unit configuration Ω' is rotated out of the normal plane of the unit with the reference point as the reference point to reverse the rotation angle θ op and the direction of rotation n op , according to the obtained unit configuration Ω", the angle and direction are calculated as follows:

[0111]

[0112] Finally, the rotation displacement in the rigid body plane is eliminated, and the unit configuration Ω" is calculated according to the unit normal vector n a After rotation, the unit configuration Ω"' is obtained after eliminating the rigid body displacement, and the rotation angle θ ip is the average rotation angle of the three mass points of the unit relative to the centroid of the unit, and the pure deformation of the unit is obtained as follows:

[0113] Δu i =x i ”'-x i a

[0114] The strain increment and stress increment can be further calculated through the unit pure deformation and the constitutive relationship of the structural material. First, a local coordinate system is established based on the unit pure deformation. The transformation matrix T between the global coordinate system and the local coordinate system is determined to obtain the membrane unit plane strain increment Combined with the material constitutive relationship, the plane stress increment of the membrane unit can be calculated Then, the unit internal force is calculated by the principle of virtual work equality and the unit force balance condition particle calculation Through the transformation matrix and virtual forward motion, the configuration Ω can be obtained b The internal force of the particle f b .

[0115] Similar to the particle motion analysis, when the time step is small enough, it can be assumed that the particles are in dynamic equilibrium in each time iteration step during the structural motion deformation process, and the motion of any particle follows Newton's second law, whose equation is:

[0116]

[0117] In the formula, is the mass assigned to the ith particle, is the acceleration of the ith particle, is the external force on the ith particle, is the internal force of the ith particle, is the contact force between the particle and the membrane at the ith particle, is the damping force of the ith particle. By using the explicit central difference algorithm, the iterative solution within a single step is avoided, and the displacement of the particle within the time step is directly obtained, and the position of the structure and the unit deformation at the next moment are obtained.

[0118] The present invention realizes the dynamic analysis of the coupling between the particle system and the membrane structure. A model of the coupling between the particle and the membrane structure is established; the contact judgment problem of the large deformation of the membrane structure and the point-to-surface contact is considered, the calculation is convenient and efficient, and a complete set of dynamic analysis methods for the coupling between the particle system and the membrane structure is completed. The analysis results of this method can be used as a reference for the design of the membrane structure, supplementing the current analysis method of the bagging effect in the design of the membrane structure, and providing further guarantee for the functional promotion and safe use of the membrane structure.

[0119] The embodiments described above provide a detailed description of the technical solutions of the present invention. It should be understood that the above are only specific embodiments of the present invention and are not intended to limit the present invention. Any modifications, supplements or similar substitutions made within the scope of the principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A dynamic analysis method for coupling a particle system with a membrane structure, characterized in that: The following steps are involved: (1) The particle motion is represented by the particle center motion, and the particles are simulated by discrete units. The membrane structure is divided into several independent membrane units, and the intersection points between the membrane units are the membrane unit mass points. The coupling between the particle system and the membrane structure is simulated by the contact unit. The contact unit is a non-solid unit that coincides with the membrane unit and is used for contact judgment and contact force calculation between the particle and the membrane unit. (2) Preliminarily screen the potential contact particles of each membrane unit through global search, determine the global coordinates of the potential contact particles, divide the responsible range of the membrane unit, calculate the local coordinates of the potential contact particles within the responsible range of the membrane unit, determine the membrane unit to which the particle belongs based on the local coordinates and judge the actual contact relationship between the particle and the membrane unit to which it belongs, calculate the contact force between the particle and the membrane unit to which it belongs, apply the contact force to the particle's center of mass, and distribute the contact force through the weighted coefficient and reversely apply it to the membrane unit mass point; (3) calculating the contact force between particles in the particle system and applying the contact force to the particle mass center; judging the movement of the particle mass center according to the mass of the particle, the external force on the particle, the contact force between the particle and the membrane unit to which it belongs in step (2), and the damping force; (4) The membrane structure is analyzed by the finite particle method, and the internal force of the membrane unit is calculated to obtain the internal force of the membrane unit particle. The movement of the membrane unit particle is determined based on the mass distributed to the membrane unit particle, the external force of the membrane unit particle, the internal force of the membrane unit particle, the contact force with a weighted coefficient in step (2), and the damping force. Further, the displacement and deformation of the membrane structure are obtained based on the movement of the membrane unit particle.

2. The dynamic analysis method of the particle system and membrane structure coupling according to claim 1 is characterized in that: The membrane plane is divided by grids and oblique lines to obtain triangular plane units, which are used as membrane units, and the three vertices of the triangular plane units are used as membrane unit mass points.

3. The dynamic analysis method of the particle system and membrane structure coupling according to claim 1 is characterized in that: In step (2), the division method of the membrane unit responsible range is: based on the membrane unit mass points i, j, k, respectively calculate the average vector n of the membrane unit normal vector connected to the membrane unit mass points i, j, k i ,n j ,n k , and n i ,n j ,n k is the particle normal vector. Based on the particle, six vertices are obtained by extending the particle normal vector in the positive and reverse directions, and the six vertices are connected by straight line segments to form the responsible range of the membrane unit.

4. The dynamic analysis method for coupling a particle system with a membrane structure according to claim 1, characterized in that: By constructing the isoparametric unit in the range of the membrane unit, the isoparametric inverse iteration method is used to construct the forward and inverse transformation function u of the global coordinates and local coordinates of the potential contact particles. + =∑N i (ξ,η,ζ)u i and After iterative calculation, the local coordinates (ξ,η,ζ) of the potential contact particles within the membrane unit are obtained; where the global coordinates of the potential contact particles are (x,y,z), u + is the global coordinate value of any point within the membrane unit’s range, u - is the local coordinate value of any point within the membrane unit’s range, u i is the coordinate of the membrane unit point i, N i (ξ,η,ζ) is the shape function with local coordinates (ξ,η,ζ) as independent variables, It is a shape function with global coordinates (x, y, z) as independent variables.

5. The dynamic analysis method of the particle system and membrane structure coupling according to claim 1 is characterized in that: The method for determining the membrane unit to which a particle belongs is as follows: when the local coordinates (ξ, η, ζ) of the potential contact particle satisfy ξ>-1, η>-1 and ξ+η<0, the particle belongs to the scope of responsibility of the membrane unit.

6. The dynamic analysis method for coupling a particle system with a membrane structure according to claim 1, characterized in that: The embedding depth of the particle on the plane of the membrane unit is calculated. When the embedding depth is greater than zero, it is determined that the particle is in contact with the membrane structure. The contact force between the particle and the membrane unit to which it belongs is calculated. The contact force includes the point-to-surface normal contact force and the point-to-surface tangential contact force. The point-to-surface normal contact force is calculated using the penalty function method, and the point-to-surface tangential contact force is calculated using the Benson friction model.

7. The dynamic analysis method for coupling a particle system with a membrane structure according to claim 1, characterized in that: In step (3), firstly, potential contact particle pairs are established. By comparing the distance between the center of mass of the potential contact particle pairs and the sum of the radii, the relative position relationship of the potential contact particle pairs is obtained, the actual contact relationship between the particles is judged, and the actual contact particle pairs are determined and used to calculate the contact force between the particles.

8. The dynamic analysis method for coupling a particle system with a membrane structure according to claim 1, characterized in that: The particle motion control equation is used to determine the particle center of mass motion. The particle motion control equation is: in, In the formula, is the mass of the ith particle, is the mass center acceleration of the ith particle, and They represent the external force on the ith particle, the contact force between particles, the contact force between the particle and its membrane unit, and the damping force, respectively. is the mass inertia matrix of the center of mass of the ith particle, is the angular acceleration of the center of mass of the i-th particle, is the external moment of the ith particle, is the contact torque between the ith particle and other particles, is the contact torque between the ith particle and its membrane unit, is the damping moment of the ith particle, and ζ is the damping coefficient.

9. The dynamic analysis method for coupling a particle system with a membrane structure according to claim 1, characterized in that: The membrane structure analysis method in step (4) is to deduct the rigid body translation and rotation displacement of the membrane unit by virtual inverse motion within a time step to determine the pure deformation Δu of the membrane unit within the time step. i ; Establish a local coordinate system through the pure deformation vector of the membrane unit, and determine the transformation matrix T between the global coordinate system and the local coordinate system; Determine the plane stress increment of the membrane unit in the local coordinate system through the isoparametric method, stress-strain relationship and force balance relationship The internal force of the membrane unit is calculated, and the internal force of the membrane unit particle is obtained through the transformation matrix and virtual forward motion.

10. The dynamic analysis method for coupling a particle system with a membrane structure according to claim 1, characterized in that: The displacement and deformation of the membrane structure are determined by the membrane unit mass point motion equation, which is expressed as: In the formula, is the mass assigned to the ith particle, is the acceleration of the ith particle, is the external force on the ith particle, is the internal force of the ith particle, is the contact force between the particle and the membrane on the ith particle, is the damping force of the ith particle.

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