A form-finding method for tensegrity structures based on dynamic programming

Abstract

The application belongs to the technical field of form-finding of tensegrity structures, and particularly relates to a form-finding method for tensegrity structures based on a dynamic programming method. For any tensegrity structure, the dynamic programming method is used to determine the connection method of all rod members in the configuration, the balance matrix theory analysis and the geometric stability determination are comprehensively used, and the configuration meeting the requirements of the tensegrity structure is obtained. The main steps are as follows: firstly, the configuration is determined, the number of nodes is determined, and the node coordinates are input; the connection method of the cable is determined; the set of optional rod members of the configuration is determined; the dynamic programming table is established, and the boundary conditions are filled; the problem is solved step by step according to the recursive formula, and whether it is a tensegrity is determined according to the constraint conditions such as the balance matrix theory analysis and the geometric stability determination; and finally, the mode of all feasible rod member combinations of the determined configuration is output.

Description

A dynamic programming-based method for form finding of tensioned integral structures Technical Field

[0001] This invention belongs to the field of form-finding technology for tensioned integral structures, specifically relating to a form-finding method for tensioned integral structures based on dynamic programming. Background Technology

[0002] Tensioned monolithic structures are spatial force-bearing structural systems composed of compression members and tension cables. Stiffness is generated through internal prestressing, and the internal forces within each element must satisfy nodal equilibrium. This equilibrium relationship depends not only on the element internal forces but also on the structure's geometry. The process of finding the form of a tensioned monolithic structure is simultaneously a process of finding its forces. In specific form-finding methods, internal forces or shape can be used as variable parameters. Commonly used form-finding methods include the force density method, the nonlinear finite element method, and the dynamic relaxation method. Finding the forces primarily involves searching for feasible prestresses or optimizing prestresses.

[0003] Currently, existing shape-finding methods often fail to fully capture the overall tensile configuration after the outer surface has been determined, and there are many repetitive results. Summary of the Invention

[0004] This invention provides a dynamic programming-based method for finding the form of a tensioned integral structure. This method can effectively calculate all feasible combinations of symmetrical and asymmetrical connections of internal members to obtain a stable structure.

[0005] The technical solution adopted by this invention to solve its technical problem is: a dynamic programming-based method for finding the shape of a tensioned integral structure. This method is for finding the shape of a configuration where only one member is connected to the same node, and specifically includes the following steps:

[0006] Step S1: Determine the basic parameters;

[0007] The basic parameters include the required shape structure, the number of nodes (node_num), and the node coordinates;

[0008] First, determine the required shape structure. Based on the determined structure, obtain all the nodes. Based on all the nodes obtained, obtain the number of nodes (node_num) and the corresponding node coordinates of each node. Input the node coordinates of each node into the programming platform.

[0009] Step S2: Select the cable connection method;

[0010] Step S3: Create the Rodset set:

[0011] Step S3-1: Determine the optional member set. The optional member set is formed by connecting all nodes of the configuration determined in step S1 in pairs to form members, and then removing the defined cable members and outer surface members. The remaining members constitute the optional member set.

[0012] Step S3-2: Based on the determined set of optional members, obtain the number of member length types k in the set of optional members. g ;

[0013] Step S3-3: Select k as the maximum number of member length types in the final tensioned overall structure. s , satisfying k s ≤k g ;

[0014] Step S3-4: Combining the set of optional members determined in step S3-1 and the number of member length types in the set of optional members obtained in step S3-2, we get k. g and the k selected in step S3-3 s ,get There are three sets, Rodset1, Rodset2, ..., Rodset3, Rodset4, Rodset5, Rodset6, Rodset7, Rodset8, Rodset9, Rodset1, Rodset1, Rodset2, Rodset9, Rodset1, Rodset2 ...9, Rodset1, Rodset2, Rodset3, Rodset4, Rodset5, Rodset6, The set of bar-like lengths

[0015] Step S4: Create a dynamic programming table dp:

[0016] Step S4-1: Based on Rodset1, Rodset2, etc. obtained in steps S3-4... The number of dynamic programming tables to be created is determined as follows:

[0017] Step S4-2: Based on the number of Rodsets obtained in Step S3-4 Given the number of nodes node_num determined in step S1, determine the number of rows in each dynamic programming table dp, dp1, dp2, ... The number of rows are |Rodset1| rows, |Rodset2| rows, and so on. In each dynamic programming table (dp) created, the number of columns is node_num / 2.

[0018] Step S4-3: Based on the number of dynamic programming tables to be created as determined in Step S4-1 and the number of rows and columns of the corresponding dynamic programming tables as determined in Step S4-2, create Rodset1, Rodset2, ... The corresponding dynamic programming tables are dp1, dp2, ...

[0019] Among them, the problem stored in the cell at the i-th row and j-th column of the dynamic programming table is dp n (i, j), and dp n (i, j) refers to the set of rod lengths of the n-th type of rod, Rodset n Among the first i groups of rods, select j groups of rods, which is the set of all feasible combinations;

[0020] Step S4-4: Input boundary conditions into the dynamic programming tables dp1, dp2... established in step S4-3 respectively;

[0021] Step S5: According to the recurrence formula, for the dynamic programming tables dp1, dp2... established in step S4-3 starting from the boundary conditions respectively, gradually solve the problem to obtain all feasible combinations that finally satisfy the structural constraints in each established dynamic programming table. The structural constraints refer to prestress balance and geometric stability;

[0022] [[ID=2O]]Step S6: According to all the feasible combinations in the final solution obtained in step S5, judge and delete the repeated configurations, output the feasible combinations, and jointly form a tensegrity structure with the cables in step S2.

[0023] As a further preference of the present invention, the boundary conditions input in step S4-4 refer to: when i < j, the feasible combinations in dp n (i, j) are an empty set. When j = 1, there are i feasible combinations in dp n (i, j), which are the first i rods of the set Rodset n of the n-th type of rod length.

[0024] As a further preference of the present invention, after inputting the boundary conditions in step S4-4, the lower right corners of the dynamic programming tables dp1, dp2... dp1[|Rodset1|][node_num / 2], all store problems, which are respectively all feasible solutions of selecting node_num / 2 rods from the set Rodset1 of the first type of rod length and jointly forming a tensegrity with the cables; all feasible solutions of selecting node_num / 2 rods from the set Rodset2 of the second type of rod length and jointly forming a tensegrity with the cables... from the set of the type of rod length

[0025] As a further preference of the present invention, the recurrence formula in step S5 is as follows:

[0026] dpn [i][j]=dp n [i-1][j]∪judge(dp n [i-1][j-1])

[0027] Among them, judge(dp) n [i-1][j-1]) represents the set of Rodsets containing the lengths of the nth type of rods. n The i-th member is placed in dp n Among the feasible combinations of [i-1][j-1], a new feasible combination is obtained after judgment;

[0028] The criterion for judgment is structural constraints. When j < node_num / 2, it is verified that the j-group members do not share nodes or intersect; when j = node_num / 2, it is verified that the j-group members do not share nodes or intersect and that the resulting structure has balanced prestress and is geometrically stable.

[0029] As a further preferred embodiment of the present invention, the specific steps of the recursion in step S5 are as follows:

[0030] Step S5-1: Solve the problem step by step using the dynamic programming table dp1.

[0031] Step S5-1-1: Initialize i and j: i = 2, j = 2;

[0032] Step S5-1-2: The combination in dp1(i,j) is equal to the combination in dp1(i-1,j);

[0033] Step S5-1-3: Given that dp1(i-1, j-1) has e combinations in step S5-1-2, dp1(i-1, j-1) k Let k be the kth feasible combination in dp1(i-1, j-1); initialize k, where k is a positive integer, starting from 1 and going up to e;

[0034] Step S5-1-4: Determine k m k m Let k be the value of step S5-1-4 for the mth time, where k = m, m is the number of times step S5-1-4 is performed, and m is a positive integer, starting from 1 and taking values ​​sequentially.

[0035] Step S5-1-5: Based on k determined in step S5-1-4 m In dp1(i-1, j-1) at the k-th position m Add the i-th member from Rodset1 to each feasible combination to obtain a new combination;

[0036] Step S5-1-6: Judge the new combination obtained in step S5-1-5. Determine whether the new combination satisfies the conditions of no intersection and no shared nodes. If it satisfies the conditions, proceed to step S5-1-7; otherwise, proceed to step S5-1-10.

[0037] Step S5-1-7: Determine whether j = node_num / 2 is satisfied. If it is satisfied, proceed to step S5-1-8; otherwise, proceed to step S5-1-9.

[0038] Step S5-1-8: Perform equilibrium matrix theory analysis and geometric stability determination. If the prestress of the structure is in equilibrium and geometrically stable, proceed to step S5-1-9. If not, proceed to step S5-1-10.

[0039] Step S5-1-9: Prove that the new combination obtained in step S5-1-5 is feasible, and store it in dp1(i,j);

[0040] Step S5-1-10: Determine the value of k determined in step S5-1-4. m Does k satisfy? m =size(dp1(i-1, j-1)), if satisfied, proceed to step S5-1-11; otherwise, return to step S5-1-4 for k. m Re-evaluate;

[0041] Step S5-1-11: Check again whether j = node_num / 2 is satisfied. If it is satisfied, proceed to step S5-1-12. If it is not satisfied, return to step S5-1-2 and increment j by 1 to obtain the revalued j. a ;

[0042] j a =j a-1 +1, where a is the number of times step S5-1-2 has been performed since step S5-1-11, plus 1; j a Let j be the value of j when returning from step S5-1-11 to step S5-1-2 for the a-th time; j a-1 The value of j in the previous step S5-1-2 when returning from step S5-1-11 to step S5-1-2 for the a-th time;

[0043] Step S5-1-12: Determine if i = size(Rodset1) satisfies the condition. If it does, the recursion ends. If not, return to step S5-1-2 and increment i by 1 to obtain the revalued i. b j = 2;

[0044] i b =i b-1+1, b is the number of times step S5-1-2 is performed after returning from step S5-1-12, plus 1, i b Let i be the value of i when returning from step S5-1-12 to step S5-1-2 for the bth time; i b-1 The value of i in the previous step S5-1-2 when returning from step S5-1-12 to step S5-1-2 for the bth time;

[0045] Step S5-2: Refer to step S5-1 to process the dynamic programming table dp2... Solve the problem step by step.

[0046] As a further preferred embodiment of the present invention, in step S6, the repeating configuration refers to two structures that can overlap after rotation or mirroring operations.

[0047] By employing the above technical solutions, the present invention has the following beneficial effects compared to the prior art:

[0048] 1. This invention can determine the connection method of all members inside the configuration for tensioned integral structures with arbitrary symmetrical shapes through dynamic programming, and obtain a configuration that meets the requirements of the tensioned integral structure by comprehensively applying the equilibrium matrix theory analysis and geometric stability judgment.

[0049] 2. This invention can remove not only repeating structures but also mirrored structures, making the shape finding results more accurate. Attached Figure Description

[0050] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0051] Figure 1 is a flowchart of the present invention;

[0052] Figure 2 is a schematic diagram of the recursive process of the present invention;

[0053] Figure 3 is a structural diagram of Embodiment 1 of the present invention;

[0054] Figure 4 is a schematic diagram of the cable connection method in Embodiment 1 of the present invention;

[0055] Figure 5 is a schematic diagram of the connection method of all rods in the configuration of Embodiment 1 of the present invention;

[0056] Figure 6 shows the shape-finding results of Embodiment 1 of the present invention;

[0057] Figure 7 is a structural diagram of Embodiment 2 of the present invention;

[0058] Figure 8 is a schematic diagram of the cable connection method in Embodiment 2 of the present invention;

[0059] Figure 9 is a schematic diagram of the connection method of all rods in Embodiment 2 of the present invention;

[0060] Figure 10 is an isometric view of the first form-finding result of Embodiment 2 of the present invention;

[0061] Figure 11 is a top view of the first form-finding result of Embodiment 2 of the present invention;

[0062] Figure 12 is an isometric view of the second form-finding result of Embodiment 2 of the present invention;

[0063] Figure 13 is a top view of the second form-finding result in Embodiment 2 of the present invention;

[0064] Figure 14 is a schematic diagram of the recursive relationship of the present invention. Detailed Implementation

[0065] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, illustrating only the basic structure of the invention, and therefore only show the components relevant to the invention.

[0066] In the description of this invention, it should be understood that the terms "left side," "right side," "upper part," "lower part," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. "First," "second," etc., do not indicate the importance of the components, and therefore should not be construed as a limitation of this invention. The specific dimensions used in this embodiment are only for illustrating the technical solution and do not limit the scope of protection of this invention.

[0067] In the accompanying drawings of this implementation scheme, thin solid lines represent cable members, and thick solid lines represent compression members.

[0068] Example 1

[0069] This embodiment provides a preferred implementation scheme, a dynamic programming-based method for finding the shape of a tensioned integral structure, as shown in Figures 1 to 6. This implementation scheme is based on the MATLAB programming platform and uses the method described in this implementation scheme to solve the structure shown in Figure 3.

[0070] Step S1: Determine the basic parameters;

[0071] The basic parameters include the required shape structure, the number of nodes (node_num), and the node coordinates;

[0072] Specifically, the configuration required for shape finding in this embodiment is shown in Figure 3, which is an icosahedral configuration. Based on the determined configuration, all nodes are obtained, and the number of nodes, node_num, is 12.

[0073] The coordinates of each vertex are:

[0074] Points 1-4: (1,0,2),(-1,0,2),(1,0,-2),(-1,0,-2);

[0075] Points 5-8: (0,2,1),(0,-2,1),(0,2,-1),(0,-2,-1);

[0076] Points 9-12: (2,1,0), (-2,1,0), (2,-1,0), (-2,-1,0);

[0077] Input the node coordinates of each node into the programming platform.

[0078] Step S2: Select the connection method for the cables, a total of 24, as shown by the thin solid lines in Figure 4;

[0079] Step S3: Create the Rodset set:

[0080] Step S3-1: Determine the set of optional members, as shown by the thick solid line in Figure 5; (The set of optional members is formed by connecting all the nodes of the configuration determined in step S1 in pairs to form members, and then removing the defined cable members and outer surface members, leaving the remaining members to form the set of optional members)

[0081] Step S3-2: Based on the determined set of optional members, obtain the number of member length types k in the set of optional members. g In this implementation plan, k g =3;

[0082] Step S3-3: Select k as the maximum number of member length types in the final tensioned overall structure. s , satisfying k s ≤k g In this implementation plan, k s =1;

[0083] Step S3-4: Combining the set of optional members determined in step S3-1 and the number of member length types in the set of optional members obtained in step S3-2, we get k. g =3 and k selected in step S3-3 s =1, thus obtaining There are three sets, Rodset1, Rodset2, and Rodset3, which are sets of lengths of the first type of bar;

[0084] Specifically, the members are represented by the node numbers at both ends, and three sets of members are obtained based on the number of different length types:

[0085] Rodset1 with a length of 3.7414 = {(1,7),(1,8),...,(8,10)}, a total of 24 rods;

[0086] Rodset2 with a length of 4 = {(1,3),(2,4),...,(11,12)}, a total of 6 rods;

[0087] Rodset3 with a length of 4.4721 = {(1,4),(2,3),...,(10,11)}, a total of 6 rods.

[0088] Step S4: Establish the dynamic programming table dp:

[0089] Step S4-1: Based on Rodset1, Rodset2, and Rodset3 obtained in step S3-4, determine the number of dynamic programming tables to be established as

[0090] Step S4-2: Based on the number of sets Rodset obtained in step S3-4 and the number of nodes node_num = 12 determined in step S1, determine the number of rows of each dynamic programming table dp. The number of rows of dp1, dp2, and dp3 are |Rodset1| = 24 rows, |Rodset2| = 6 rows, and |Rodset3| = 6 rows respectively. The number of columns of each established dynamic programming table dp is node_num / 2 = 6 columns;

[0091] Step S4-3: According to the number of dynamic programming tables to be established determined in step S4-1 and the number of rows and columns of the corresponding dynamic programming tables determined in step S4-2, establish the dynamic programming tables dp1, dp2, and dp3 corresponding to Rodset1, Rodset2, and Rodset3;

[0092] Among them, the problem stored in the cell at the i-th row and j-th column of the dynamic programming table is dp n (i,j), dp n (i,j) refers to the set of all feasible combinations of selecting j groups of rods from the first i groups of rods in the set Rodset of the length of the n-th type of rod; n

[0093] Step S4-4: Input the boundary conditions into the dynamic programming tables dp1, dp2, and dp3 established in step S4-3 respectively to obtain Table 1, Table 2, and Table 3;

[0094] The boundary conditions are: when i < j, the feasible combinations in dp n (i,j) are an empty set. When j = 1, dp nThere are i feasible combinations in (i,j), which constitute the set of the nth rod length. n The first i rods.

[0095] Table 1, Dynamic Programming Table dp1 for Rodset1

[0096]

[0097] Table 2, Rodset2 Dynamic Programming Table dp2

[0098]

[0099] Table 3, Rodset3 Dynamic Programming Table dp3

[0100]

[0101]

[0102] After inputting the boundary conditions, the lower right corners of the dynamic programming tables dp1, dp2, and dp3 contain the following problems: dp1[|Rodset1|][node_num / 2]=dp1

[24] [6], dp2[|Rodset2|][node_num / 2]=dp2[6][6], and dp3[|Rodset3|][node_num / 2]=dp3[6][6]. These problems are: all feasible solutions for selecting 6 members from the set of first-type member lengths Rodset1 and forming a tensioned whole with the cable; all feasible solutions for selecting 6 members from the set of second-type member lengths Rodset2 and forming a tensioned whole with the cable; and all feasible solutions for selecting 6 members from the set of third-type member lengths Rodset3 and forming a tensioned whole with the cable.

[0103] Step S5: According to the recursive formula, solve the problem step by step for the dynamic programming tables dp1, dp2, and dp3 established in Step S4-3, starting from the boundary conditions, to obtain all feasible combinations that finally satisfy the structural constraints (structural constraints refer to prestress equilibrium and geometric stability) for each established dynamic programming table; that is, solve step by step from the upper left to the lower right of each table according to the recursive formula (as shown in the flowchart steps in Figure 2) to obtain the final combination.

[0104] The output determines all feasible combinations of rods for the configuration and filters out symmetrical and mirror configurations, finally obtaining one configuration with rods as follows: (1,3), (2,4), (5,6), (7,8), (9,10), (11,12), as shown in Figure 6.

[0105] The recursive formula is as follows:

[0106] dp n [i][j]=dp n [i-1][j]∪judge(dp n [i-1][j-1])

[0107] Among them, judge(dp) n [i-1][j-1]) represents the set of Rodsets containing the lengths of the nth type of rods. n The i-th member is placed in dp n Among the feasible combinations of [i-1][j-1], a new feasible combination is obtained after judgment;

[0108] The criterion for judgment is structural constraints. When j < node_num / 2, it is verified that the j-group members do not share nodes or intersect; when j = node_num / 2, it is verified that the j-group members do not share nodes or intersect and that the resulting structure has balanced prestress and is geometrically stable.

[0109] The specific steps of the recursion shown in Figure 14 are as follows:

[0110] Step S5-1: Solve the problem step by step using the dynamic programming table dp1.

[0111] Step S5-1-1: Initialize i and j: i = 2, j = 2;

[0112] Step S5-1-2: The combination in dp1(i,j) is equal to the combination in dp1(i-1,j);

[0113] Specifically, dp1(i,j) is dp1(2,2), and dp1(i-1,j) is dp1(1,2), that is, the combination in dp1(2,2) is equal to the combination in dp1(1,2).

[0114] Step S5-1-3: Given that dp1(i-1, j-1) has e combinations in step S5-1-2, dp1(i-1, j-1) k Let k be the kth feasible combination in dp1(i-1, j-1); initialize k, where k is a positive integer, starting from 1 and going up to e;

[0115] Specifically, dp1(i-1, j-1) is dp1(1, 1), dp1(1, 1) has 1 combination, and k takes the value 1.

[0116] Step S5-1-4: Determine k m k mLet k be the value of step S5-1-4 for the mth time, where k = m, m is the number of times step S5-1-4 is performed, and m is a positive integer, starting from 1 and taking values ​​sequentially.

[0117] Specifically, m = 1, k m =1.

[0118] Step S5-1-5: Based on k determined in step S5-1-4 m =1, add the i-th member of Rodset1 to the first feasible combination of dp1(1,1) to obtain a new combination;

[0119] Step S5-1-6: Judge the new combination obtained in step S5-1-5. Determine whether the new combination satisfies the conditions of no intersection and no shared nodes. If it satisfies the conditions, proceed to step S5-1-7; otherwise, proceed to step S5-1-10.

[0120] Step S5-1-7, j=2, determine whether j satisfies j=node_num / 2=6. If it satisfies, proceed to step S5-1-8; otherwise, proceed to step S5-1-9.

[0121] Step S5-1-8: Perform equilibrium matrix theory analysis and geometric stability determination. If the prestress of the structure is in equilibrium and geometrically stable, proceed to step S5-1-9. If not, proceed to step S5-1-10.

[0122] Step S5-1-9: Prove that the new combination obtained in step S5-1-5 is feasible and store it in dp1(i,j); that is, store the new combination obtained in step S5-1-5 as feasible in dp1(2,2).

[0123] Step S5-1-10: Determine the value of k determined in step S5-1-4. m =1, does k satisfy? m =size(dp1(i-1, j-1)), if satisfied, proceed to step S5-1-11; otherwise, return to step S5-1-4 for k. m Re-evaluate;

[0124] k m When =1, 1 = k m =size(dp1(1,1)) to perform step S5-1-11.

[0125] Step S5-1-11: Check again whether j satisfies j = node_num / 2 = 6. If it does, proceed to step S5-1-12. If it does not, return to step S5-1-2 and increment j by 1 to obtain the revalued j. a ;

[0126] j=2 does not satisfy j=node_num / 2=6, so return to step S5-1-2 to increment j by 1 to obtain the new value of j. a =3;

[0127] j a =j a-1 +1, where a is the number of times step S5-1-2 has been performed since step S5-1-11, plus 1; j a Let j be the value of j when returning from step S5-1-11 to step S5-1-2 for the a-th time; j a-1 The value of j in the previous step S5-1-2 when returning from step S5-1-11 to step S5-1-2 for the a-th time;

[0128] Step S5-1-12: Determine if i satisfies i = size(Rodset1) = 24. If it does, the recursion ends. If it does not, return to step S5-1-2 and increment i by 1 to obtain the revalued i. b j = 2;

[0129] Since i = 2 does not satisfy i = size(Rodset1) = 24, we return to step S5-1-2 and increment i by 1 to obtain the new value of i. b =3, j=2;

[0130] i b =i b-1 +1, b is the number of times step S5-1-2 is performed after returning from step S5-1-12, plus 1, i b Let i be the value of i when returning from step S5-1-12 to step S5-1-2 for the bth time; i b-1 The value of i in the previous step S5-1-2 when returning from step S5-1-12 to step S5-1-2 for the bth time;

[0131] Step S5-2: Refer to step S5-1 to solve the dynamic programming tables dp2 and dp3 step by step.

[0132] Step S6: Based on the feasible combinations in the final solution, identify and delete repeating configurations, output feasible combinations, and combine them with the cables from step S2 to form a tensioned overall structure. Repeating configurations refer to two structures that can overlap after rotation or mirroring operations.

[0133] Example 2

[0134] This embodiment provides a preferred implementation scheme. A dynamic programming-based method for finding the shape of a tensioned integral structure is shown in Figure 1 and Figures 7 to 13. This implementation scheme is based on the MATLAB programming platform and uses the method described in this invention to solve the structure shown in Figure 7.

[0135] Step S1: Determine the basic parameters;

[0136] The basic parameters include the required shape structure, the number of nodes (node_num), and the node coordinates;

[0137] Specifically, the configuration required for shape finding in this embodiment is shown in Figure 7, which is a torsion octagonal prism configuration. Based on the determined configuration, all nodes are obtained, and the number of nodes node_num is 16.

[0138] The coordinates of each vertex are:

[0139] Points 1~8: (cos(45×i) sin(45×i) 0), i=1,2,...,8;

[0140] Points 9~16: (cos(45°×i+22.5°) sin(45°×i+22.5°) 1),i=9,10,...,16;

[0141] Input the node coordinates of each node into the programming platform.

[0142] Step S2: Select the connection method for the cables, a total of 24, as shown by the thin solid lines in Figure 8;

[0143] Step S3: Create the Rodset set:

[0144] Step S3-1: Determine the set of optional members, as shown by the thick solid line in Figure 9;

[0145] Step S3-2: Based on the determined set of optional members, obtain the number of member length types k in the set of optional members. g In this implementation plan, k g =3;

[0146] Step S3-3: Select k as the maximum number of member length types in the final tensioned overall structure. s , satisfying k s ≤k g In this implementation plan, k s =3;

[0147] Step S3-4: Combining the set of optional members determined in step S3-1 and the number of member length types in the set of optional members obtained in step S3-2, we get k. g =3 and k selected in step S3-3 s =1, thus obtaining There are three sets, Rodset, which are sets of lengths of the first type of rod;

[0148] Specifically, the members are represented by the node numbers at both ends, and a set of members is obtained based on the number of different length types:

[0149] Rodset1 = {(1,15),(2,16),...,(8,12)}, with a total of 40 rods.

[0150] Step S4: Create a dynamic programming table dp:

[0151] Step S4-1: Based on Rodset1 obtained in Step S3-4, determine the number of dynamic programming tables that need to be built.

[0152] Step S4-2: Based on the number of Rodsets obtained in Step S3-4 Given the number of nodes determined in step S1, node_num = 16, determine the number of rows in the dynamic programming table dp. The number of rows in dp1 is |Rodset1| = 40 rows, and the number of columns is node_num / 2 = 8 columns.

[0153] Step S4-3: Based on the number of dynamic programming tables to be established as determined in step S4-1 and the number of rows and columns of the corresponding dynamic programming table determined in step S4-2, establish the dynamic programming table dp1 corresponding to Rodset1;

[0154] Step S4-4: Input the boundary conditions into the dynamic programming table dp1 established in step S4-3 to obtain Table 4;

[0155] The dynamic programming table dp1 built based on Rodset1 above is as follows:

[0156] Table 4, Rodset1 Dynamic Programming Table dp1

[0157]

[0158]

[0159] The problem is stored in the lower right corner of the dynamic programming table dp1 after inputting the boundary conditions, dp1[|Rodset1|][node_num / 2]=dp1

[40] [8]. The problem is to select node_num / 2=8 members from the set of first-class member lengths Rodset1, and together with the cable, form all feasible solutions for the tensioning whole.

[0160] Step S5: According to the recursive formula, solve the problem step by step from the boundary conditions for the dynamic programming table dp1 established in step S4-3 to obtain all feasible combinations of the dynamic programming table dp1 that finally satisfy the structural constraints (structural constraints refer to prestress equilibrium and geometric stability); that is, solve step by step from the upper left to the lower right of each table according to the recursive formula (as shown in the flowchart in Figure 2) to obtain the final combination.

[0161] The output determines all feasible combinations of rods for the configuration and filters out symmetrical and mirror configurations, resulting in two configurations. One configuration has the following rods: (1,12), (2,13), (3,14), (4,15), (5,16), (6,9), (7,10), (8,11) (as shown in Figures 10 and 11); the other configuration has the following rods: (1,13), (2,12), (3,15), (4,14), (5,9), (6,16), (7,11), (8,10) (as shown in Figures 12 and 13).

[0162] Those skilled in the art will understand that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the meaning consistent with their meaning in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0163] The meaning of "and / or" as used in this application includes both situations where each exists alone or both exist simultaneously.

[0164] The term "connection" as used in this application can mean a direct connection between components or an indirect connection between components through other components.

[0165] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for form finding of a tensioned integral structure based on dynamic programming, characterized in that, This form-finding method is for configurations where only one member is connected to the same node. Specifically, it includes the following steps: Step S1: Determine basic parameters; these parameters include the required configuration, the number of nodes (node_num), and node coordinates. First, determine the required configuration. Based on the determined configuration, obtain all nodes. Then, obtain the number of nodes (node_num) and the corresponding node coordinates. Input the node coordinates of each node into the programming platform. Step S2: Select the cable connection method. Step S3: Establish a set (Rodset): Step S3-1: Determine the optional member set. The optional member set is formed by connecting all nodes of the configuration determined in Step S1 in pairs to form components, excluding the defined cable components and outer surface components. The remaining components constitute the optional member set. Step S3-2: Based on the determined optional member set, obtain the number of member length types (k) in the optional member set. g Step S3-3: Select k as the maximum number of member length types in the final tensioned overall structure. s , satisfying k s ≤k g Step S3-4: Combining the set of optional members determined in step S3-1 and the number of member length types in the set of optional members obtained in step S3-2, we get k. g and the k selected in step S3-3 s ,get There are three sets, Rodset1, Rodset2, ..., Rodset3, Rodset4, Rodset5, Rodset6, Rodset7, Rodset8, Rodset9, Rodset1, Rodset1, Rodset2, Rodset9, Rodset1, Rodset2, Rodset8, Rodset9, Rodset1, Rodset1, Rodset2, Rodset9, Rodset1, Rodset2, Rodset9, Rodset1, Rodset2, Rodset3, Rodset4, Rodset5, Rodset6, Rodset7, Rodset8 ... The set of bar-like lengths Step S4, establish the dynamic programming table dp: Step S4-1, based on the results obtained in steps S3-4 The number of dynamic programming tables to be created is determined as follows: Step S4-2: Based on the number of Rodsets obtained in Step S3-4 Given the number of nodes node_num determined in step S1, determine the number of rows in each dynamic programming table dp, where dp1, dp2, ... have |Rodset1| rows, |Rodset2| rows, and so on. Each dynamic programming table (dp) created has 2 columns (node_num / 2). Step S4-3: Based on the number of dynamic programming tables required in step S4-1 and the number of rows and columns of the corresponding dynamic programming table determined in step S4-2, create... The corresponding dynamic programming tables are dp1, dp2, ...; where the problem stored in the cell of the i-th row and j-th column of the dynamic programming table is dp. n (i,j), dp n (i,j) refers to the Rodset containing the lengths of the nth type of rod. n In the first group of members, select group j, which is the set of all feasible combinations; in step S4-4, input the boundary conditions into the dynamic programming tables dp1, dp2, ... established in step S4-3 respectively; in step S5, according to the recursive formula, solve the problem step by step for the dynamic programming tables dp1, dp2, ... established in step S4-3, starting from the boundary conditions, to obtain all feasible combinations that finally satisfy the structural constraints for each dynamic programming table. The structural constraints refer to prestress equilibrium and geometric stability; in step S6, based on all feasible combinations in the final solution obtained in step S5, identify and delete duplicate configurations, output feasible combinations, and together with the cables in step S2, form a tensioned integral structure.

2. The method for form finding of a tensioned integral structure based on dynamic programming according to claim 1, characterized in that: The boundary conditions input in step S4-4 refer to: when <j, dp n (i, j) the set of feasible combinations is an empty set, when j = 1, dp n (i, j) there is a set of feasible combinations, which is the set Rodset of the lengths of the nth type of bars n the first bars in 3. The method for form finding of a tensioned integral structure based on dynamic programming according to claim 1, characterized in that: In step S4-4, after inputting the boundary conditions, the bottom right corner of the dynamic programming table dp1, dp2... is dp1[|Rodset1|][node_num / 2]. The problem is stored in the middle, which is to select node_num / 2 members from the set of lengths of the first type of members Rodset1, and form all feasible solutions with the cable to form the tensioned whole; From Rodset2, select node_num / 2 members of type 2, and combine them with the cable to form all feasible solutions for the tensioned system... The set of bar-like lengths Select node_num / 2 members and combine them with the cable to form all feasible solutions for the tensioned system.

4. The method for form finding of a tensioned integral structure based on dynamic programming according to claim 2, characterized in that, The recursive formula in step S5 is as follows: dp n [i][j]=dp n [i-1][j]judge(dp n [i-1][j-1]) where, judge(dp n [i-1][j-1]) represents the set of Rodsets containing the lengths of the nth type of rods. n The first member is placed in dp n Among the feasible combinations of [i-1][j-1], a new feasible combination is obtained after judgment. The judgment criterion is the structural constraint. When j < node_num / 2, it is verified that the j group of members do not share nodes or intersect. When j = node_num / 2, it is verified that the j group of members do not share nodes or intersect and the resulting structure has balanced prestress and is geometrically stable.

5. The method for form finding of a tensioned integral structure based on dynamic programming according to claim 4, characterized in that, The specific steps of the recursion in step S5 are as follows: Step S5-1, Solve the problem step by step using the dynamic programming table dp1; Step S5-1-1, Initialize j:=2, j=2; Step S5-1-2, The combination in dp1(i,j) is equal to the combination in dp1(i-1,j); Step S5-1-3, Given that dp1(i-1,j-1) has e combinations in step S5-1-2, dp1(i-1,j-1)... k Find the k-th feasible combination in dp1(i-1, j-1); initialize k, where k is a positive integer, starting from 1 and going up to e; step S5-1-4, determine k m k m Let k be the value of step S5-1-4 for the m-th iteration, where k = m, m is the number of times step S5-1-4 has been performed, and m is a positive integer starting from 1; Step S5-1-5, based on k determined in step S5-1-4. m In dp1(i-1, j-1) at the k-th position m Add the i-th member from Rodset1 to the feasible combinations to obtain a new combination; Step S5-1-6: Judge the new combination obtained in step S5-1-5 to determine whether it satisfies the conditions of non-intersecting and non-shared nodes. If it satisfies these conditions, proceed to step S5-1-7; otherwise, proceed to step S5-1-10; Step S5-1-7: Judge whether j = node_num / 2 is satisfied. If it is satisfied, proceed to step S5-1-8; otherwise, proceed to step S5-1-9; Step S5-1-8: Perform equilibrium matrix theory analysis and geometric stability determination. If the prestress of the structure is balanced and geometrically stable, proceed to step S5-1-9; otherwise, proceed to step S5-1-10; Step S5-1-9: Prove that the new combination obtained in step S5-1-5 is feasible and store it in dp1(i,j); Step S5-1-10: Judge the k determined in step S5-1-4. m Does k satisfy? m =size(dp1(i-1, j-1)), if satisfied, proceed to step S5-1-11; otherwise, return to step S5-1-4 for k. m Perform a new value selection; Step S5-1-11: Check again whether j = node_num / 2 is satisfied. If satisfied, proceed to step S5-1-12; otherwise, return to step S5-1-2 and increment j by 1 to obtain the new value j. a ;j a =j a-1 +1, where a is the number of times step S5-1-2 has been performed since step S5-1-11, plus 1; j a Let j be the value of j when returning from step S5-1-11 to step S5-1-2 for the a-th time; j a-1 Let j be the value of the previous step in step S5-1-2 when returning from step S5-1-11 to step S5-1-2 for the a-th time; Step S5-1-12: Determine if i = size(Rodset1) is satisfied. If it is satisfied, the recursion ends; if it is not satisfied, return to step S5-1-2 and increment i by 1 to obtain the revalued i. b j = 2; i b =i b-1 +1, b is the number of times step S5-1-2 is performed after returning from step S5-1-12, plus 1, i b Let i be the value of i when returning from step S5-1-12 to step S5-1-2 for the bth time; i b-1 For the b-th time, return from step S5-1-12 to step S5-1-2, referring to the previous time i returned from step S5-1-12 to step S5-1-2; Step S5-2, refer to step S5-1 to modify the dynamic programming table. Solve the problem step by step.

6. The method for form finding of a tensioned integral structure based on dynamic programming according to claim 1, characterized in that: In step S6, repeating configuration refers to two structures that can overlap after rotation or mirroring operations.

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