A large deformation calculation method for a rod system structure based on Euler method

Abstract

The application relates to a large deformation calculation method of a rod system structure based on an Euler method, which comprises the following steps: obtaining structure information to be analyzed and discretizing and dividing units; solving an elastic stiffness matrix of each unit under a local coordinate system and assembling the whole stiffness matrix; adding boundary conditions and applying external force, establishing a structure stiffness equation, and solving the displacement of the structure under a small deformation condition; establishing the whole coordinate system and the local coordinate system of the unit and their connection according to the structure position after deformation, and determining the coordinate conversion matrix; determining the large deformation correction matrix of the rod system structure; correcting the elastic stiffness matrix of the unit by using the large deformation correction matrix of the rod system structure and the coordinate conversion matrix, establishing a new structure stiffness equation based on a finite element calculation method and Euler description, and setting a convergence criterion to carry out iterative calculation on the equation, and obtaining the displacement calculation result of the large deformation of the rod system structure. Compared with the prior art, the application has the advantages of high precision and high solving efficiency.

Description

Technical Field

[0001] This invention relates to the field of structural deformation calculation, and in particular to a method for calculating large deformation of bar structures based on the Euler method. Background Technology

[0002] Large structural deformation (geometric nonlinearity) is a crucial aspect of structural nonlinear analysis. Geometric nonlinearity refers to the alteration of the relationship between displacement and strain during structural deformation, especially when nodal displacements or rotations are significant. As the load increases, the stiffness of the structure continuously changes during deformation, consequently altering its equilibrium state. Under large deformation conditions, calculations using first-order linear geometric equations introduce substantial errors, necessitating the consideration of second-order or even higher-order geometric equations to improve accuracy. A key characteristic of geometric nonlinearity is the need to establish the structure's equilibrium equations at its post-deformation geometric location, which is typically unknown. When dealing with large structural deformations, it is essential to define stress and strain precisely and to select the appropriate state to describe all physical quantities. In nonlinear analysis, different reference coordinate systems result in different expressions for physical quantities before and after deformation.

[0003] Currently, the three-dimensional continuum virtual work incremental equation method is widely used in the field of geometric nonlinear analysis. This method uses finite deformation theory to describe the deformation process of a continuum, solving for the entire deformation process by progressively determining the displacement, stress, and strain increments at each stage. Starting from a known state at time T with displacement, stress, and strain, the increments of displacement, stress, and strain from time T to time T+ΔT are determined, thus obtaining the physical quantities at time T+ΔT. In the next loading step, the state at time T+ΔT becomes a known state, and the above process is repeated to obtain the state at time T+2ΔT. Through this incremental solution process, the final state of the structure and the changes throughout the process can be obtained. It is important to note that the basic unknowns in the incremental solution are the increments of each state, not the state quantities themselves. The basic equation for determining the increments is the three-dimensional virtual work incremental equation, which has two commonly used expressions: the Total Lagrangian Formulation (TL formulation) and the Updated Lagrangian Formulation (UL formulation).

[0004] The TL formulation method uses the initial state at time 0 as the reference state throughout the deformation process, establishing incremental equations accordingly. The UL formulation method assumes all state variables at time T have been obtained, using the state at time T as the reference state, then calculates the state variables at time T+ΔT, and then uses the state at T+ΔT as the reference state again to calculate the state variables at time T+2ΔT. In this way, the reference state is updated at each step, always using the currently obtained state as the reference state for the next stage of calculation. Both methods are incremental finite element formulation methods, dividing the load deformation process into a series of incremental segments. The structural load response in each incremental segment is approximately linearized, and multiple iterations are performed in the calculation of each incremental segment.

[0005] In the TL formulation method, the equations for each incremental calculation are established on the initial configuration, which may lead to convergence failure or even errors in the analysis of large rotation angle problems. Furthermore, the element stiffness matrix includes elastic stiffness, geometric stiffness, and large displacement matrices, making the process complex and cumbersome. In the UL formulation method, the two nodes of the element are transformed according to the Euler angle between the local and global coordinate systems. This results in different coordinate transformation matrices at the two ends of the element and fails to consider the influence of element bending deformation. Moreover, the coordinate transformation matrix needs to be recalculated in each iterative calculation, leading to computational inefficiency. Currently, a widely adaptable, highly accurate, and fast-converging method for calculating structural geometric nonlinear deformation is still lacking. Summary of the Invention

[0006] The purpose of this invention is to provide a method for calculating large deformation of bar structures based on the Euler method, enabling rapid and accurate calculation of large deformation displacements of the structure.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A method for calculating large deformation of bar structures based on the Euler method includes the following steps:

[0009] Step 1) Obtain the structural information to be analyzed and discretize it, dividing it into units;

[0010] Step 2) Solve for the element elastic stiffness matrix of each element in the local coordinate system, and assemble them in the global coordinate system to obtain the global stiffness matrix; add boundary conditions and apply external forces to establish the structural stiffness equation, and solve for the global displacement and nodal displacement of the structure under small deformation conditions.

[0011] Step 3) Establish the overall coordinate system and local coordinate system of the element and their relationship based on the position of the deformed structure, and determine the coordinate transformation matrix of the element;

[0012] Step 4) Determine the large deformation correction matrix of the truss structure based on the relationship between the actual internal forces and displacements during large structural deformation, the differential equation of the beam's deflection curve, and the curvature formula.

[0013] Step 5) Correct the elastic stiffness matrix of the element using the large deformation correction matrix and coordinate transformation matrix of the bar structure. Establish a new structural stiffness equation based on the finite element method and Euler description, and set a convergence criterion to iteratively calculate the equation to obtain the displacement calculation results of the large deformation of the bar structure.

[0014] The coordinate transformation matrix is:

[0015]

[0016]

[0017] Where [T] is the coordinate transformation matrix and [t] is the node transformation matrix. These are the coordinate axes of the unit's local coordinate system established based on the position of the deformed structure.

[0018] The large deformation correction matrix for the rod structure is:

[0019]

[0020] in, V is the correction matrix for large deformation of the rod structure. N α is the axial correction factor. y α z β y β z γ is the bending moment correction factor. y γ z This is the shear force correction factor.

[0021] The calculation method for correcting the element elastic stiffness matrix using the large deformation correction matrix and coordinate transformation matrix of the bar structure is as follows:

[0022]

[0023] in, It is the large deformation correction matrix for the rod structure, [k]. e [T] is the elastic stiffness matrix of the spatial beam element, [K] is the coordinate transformation matrix, and [K] is the coordinate transformation matrix. e This is the corrected element elastic stiffness matrix.

[0024] The convergence criterion is as follows:

[0025]

[0026] Where {Δa} is the displacement difference vector, and ||{Δa}|| ∞λ represents the maximum absolute value in the displacement difference vector, where λ is a very small number specified beforehand.

[0027] Compared with the prior art, the present invention has the following beneficial effects:

[0028] This invention proposes a novel method for calculating large structural deformation based on the Euler method. This method directly uses the deformed node positions as the basic unknowns and introduces a large deformation correction matrix. Compared with some existing geometric nonlinear analysis methods, the iterative calculation process is different, the theoretical process is simpler and more efficient, the convergence performance and computational efficiency are better, and the calculation results are more accurate. Attached Figure Description

[0029] Figure 1 This is a flowchart of the method of the present invention;

[0030] Figure 2 This is a schematic diagram of the initial state of a spatial beam element;

[0031] Figure 3 This is a schematic diagram of the state of a spatial beam element after deformation.

[0032] Figure 4 This is a schematic diagram of the unit coordinate system after taking the average rotation.

[0033] Figure 5 This is a schematic diagram showing the rotation of the reference axis of the cross section;

[0034] Figure 6 This is a schematic diagram of the nodal displacements and nodal forces of a spatial beam element;

[0035] Figure 7 This is a schematic diagram of a cantilever beam subjected to a concentrated force at its right end in an embodiment of the present invention;

[0036] Figure 8 This is a diagram showing the calculation results of the Euler algorithm for the cantilever beam model in an embodiment of the present invention;

[0037] Figure 9 This is a comparison diagram of the Euler algorithm and the MIDAS solution for the cantilever beam model in this embodiment of the invention;

[0038] Figure 10 This is a comparison chart of the Euler algorithm and the MIDAS solution under different dimensionless parameters in the embodiments of the present invention. Detailed Implementation

[0039] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. These embodiments are based on the technical solution of the present invention and provide detailed implementation methods and specific operating procedures. However, the scope of protection of the present invention is not limited to the following embodiments.

[0040] This embodiment provides a method for calculating large deformations of rod structures based on the Euler method, such as... Figure 1 As shown, it includes the following steps:

[0041] Step 1) Obtain the structural information to be analyzed and discretize it, dividing it into units;

[0042] Step 2) Solve for the element elastic stiffness matrix of each element in the local coordinate system, and assemble them in the global coordinate system to obtain the global stiffness matrix; add boundary conditions and apply external forces to establish the structural stiffness equation, and solve for the global displacement and nodal displacement of the structure under small deformation conditions.

[0043] Step 3) Establish the overall coordinate system and local coordinate system of the element and their relationship based on the position of the deformed structure, and determine the coordinate transformation matrix of the element;

[0044] Step 4) Determine the large deformation correction matrix of the truss structure based on the relationship between the actual internal forces and displacements during large structural deformation, the differential equation of the beam's deflection curve, and the curvature formula.

[0045] Step 5) Correct the elastic stiffness matrix of the element using the large deformation correction matrix and coordinate transformation matrix of the bar structure. Establish a new structural stiffness equation based on the finite element method and Euler description, and set a convergence criterion to iteratively calculate the equation to obtain the displacement calculation results of the large deformation of the bar structure.

[0046] In the finite element analysis of truss structures, regardless of whether the deformation is small or large, the displacements of the end nodes of the element are always used as the basic unknowns. The element interpolation function is constructed using these end node displacements to form the deformed shape of the element. Once the deformation is determined, the relationship between internal forces and displacements can be established. All of the above processes are closely related to the element's local coordinate system. In small deformation theory, the local coordinate system is fixed and independent of displacement. In large deformation theory, the local coordinate system is closely related to displacement. Therefore, in the analysis of large deformation structures, determining the position of the local coordinate system and the coordinate transformation matrix for transforming the element from the local coordinate system to the global coordinate system is the most important task. The process of establishing the global coordinate system and local coordinate system of a truss structure under large deformation conditions, and their relationship, is as follows:

[0047] The local coordinate system of the spatial beam element in the initial state is as follows: Figure 2 As shown. The x-axis is the centroidal axis, and the y-axis and z-axis are the principal axes of the cross section. The three axes satisfy the right-hand orthogonal rule. The cross sections at the i and j ends are parallel and perpendicular to the centroidal axis.

[0048] Let the initial coordinates of node i in the global coordinate system be: (x i ,y i ,z i The initial coordinates of node j are: (x j,y j ,z j The initial position vectors of points i and j are:

[0049]

[0050] The displacement of node i in the global coordinate system is:

[0051] Linear displacement: u i v i w i Angular displacement: θ ix θ iy θ iz .

[0052] The radius vector of point i after deformation is:

[0053]

[0054] in

[0055] x it =x i +u i y it =y i +v i z it =z i +w i (3)

[0056] The angular vector is:

[0057]

[0058] Similarly, the displacement of node j in the global coordinate system is:

[0059] Linear displacement: u j v j w j Angular displacement: θ jx θ jy θ jz .

[0060] The radius vector of point j after deformation is:

[0061]

[0062] in

[0063] x jt =x j +u j y jt =y j +v j z jt =z j+w j (6)

[0064] The angular vector is:

[0065]

[0066] After deformation, the original centroidal axis ij moves to position i′j′, as shown below. Figure 3 As shown.

[0067] Based on equations (2) and (6), we can determine that:

[0068]

[0069] set up Let x' be the unit vector of the x-axis, which can be determined by equation (8):

[0070]

[0071]

[0072] The orientation of the centroidal axis depends only on linear displacement and not on angular displacement; for the orientation of the cross-sections at ends i and j, it depends only on rotation, i.e., angular displacement, and not on linear displacement.

[0073] Under normal circumstances, the cross sections at ends i and j are... After rotation, the planes at both ends are no longer parallel. To ensure that the principal axes of the cross-sections at both ends are parallel, an average rotation is used for orientation positioning in the local coordinate system. After average rotation, the deformed beam element in the local coordinate system is as follows: Figure 4 As shown, the cross-sections at both ends are parallel, meaning the principal axes of the cross-sections are parallel, but the two end faces are still not perpendicular to the rod axis. With rotation, the original reference axis y now becomes y″. If the orientation of y″ is already determined, then the orientation of the local coordinate system is easily determined.

[0074] set up If y″ is the unit vector, then we have

[0075]

[0076] A local coordinate system is constructed after the beam element has deformed, with all axes perpendicular to each other. This allows us to establish the relationship between the local coordinate system and the global coordinate system.

[0077] For ease of explanation, the local coordinate system will be expressed as follows: As the centroidal principal axis, As the reference axis, Let x be the other principal axis of the cross section, and let its relationship with the global coordinate system be:

[0078]

[0079] Where [t] is the node transformation matrix, which is formed by... The local coordinate system is generated, i.e.

[0080]

[0081] The next step is to determine the orientation of y″.

[0082] Let C be the axis of rotation passing through the centroid of the cross section and be a unit vector, θ be the angle of rotation, and point A be the reference point on the principal axis of the cross section when it is not rotated. It should be noted that C and A are the positions after the linear displacement is completed.

[0083] like Figure 5 As shown, It is the reference axis of the cross section. It is the average rotation angle unit vector, Around After the axis rotates by an angle θ, it reaches It means rotation The position of the reference axis of the rear section, i.e.

[0084] Rotation angle θ and vector The calculation is as follows:

[0085]

[0086] when and When they are not collinear, perform the following operations:

[0087]

[0088] Where u is a scalar. Let:

[0089]

[0090] in

[0091]

[0092] Again

[0093]

[0094] Perform the operation:

[0095]

[0096] Where {n}T ={n x n y n z} T Then perform the calculation:

[0097]

[0098] Based on equations (19) and (20), construct the function:

[0099]

[0100] beg make:

[0101]

[0102] The specific calculation process is as follows:

[0103]

[0104] After simplification, it becomes:

[0105]

[0106] Written in matrix form:

[0107]

[0108] It is important to note that reference point A must initially lie on the principal axis of the cross section, and the reference axis should be converted to a unit vector. Right now examine and Whether they are collinear. If they are collinear, then A and C only undergo linear translation, and point A does not undergo rotation, because R = 0 in this case. when and When collinear: because Since they are collinear unit vectors, Right now That is, collinearity; the discriminant of collinearity: if When ||b|-1|<α, α is a small, predetermined number.

[0109] By solving equation (25), we can obtain... Then the position vector of point A′ is

[0110]

[0111] From equation (26), the initial reference axis After rotation Later became

[0112]

[0113] in yes The normalized vector is also From equation (11), we can obtain

[0114]

[0115] In summary, the local coordinate system after element deformation can be obtained. And its orientation in the global coordinate system.

[0116] Based on equations (12) and (13), the nodal transformation matrix [t] has been obtained. Therefore, the transformation relationship of the nodal displacement vectors of the beam element is as follows:

[0117]

[0118] Abbreviated as:

[0119]

[0120] Where [T] is the coordinate transformation matrix, {a} e It is the displacement vector of the element node in the global coordinate system. It is the displacement vector of the element node in the local coordinate system.

[0121] Under small deformation conditions, the elastic stiffness matrix of the spatial beam element in the local coordinate system is:

[0122]

[0123] In the formula, E is the elastic modulus of the material, G is the shear modulus of the material, A is the cross-sectional area of ​​the rod, l is the length of the rod, and I y The moment of inertia of the cross section in the xz plane, I z J is the moment of inertia of the cross section in the xy plane, and J is the torsional moment of inertia of the element.

[0124] In the local coordinate system, the relationship between the end forces and end displacements of the beam element is still expressed in the form under small deformation conditions, i.e.

[0125]

[0126] Where {f} is the element nodal force vector in the local coordinate system. It is the displacement vector of the element node in the local coordinate system. However, under large deformation conditions, equation (32) needs to be corrected according to the relationship between the actual internal force and displacement under large deformation. Therefore, a large deformation correction matrix is ​​introduced.

[0127] The nodal displacements and nodal forces of the spatial beam element in the local coordinate system are as follows: Figure 6 As shown.

[0128] The nodal force vector is {N} i Q iy Q iz M ix M iy M iz N i Q iy Q iz M ix M iy M iz} T .

[0129] Let l0 be the stress-free length of the beam element, and l be the deformed length of the beam element. In the calculation under small deformation conditions, the axial strain of the beam element is: In practice, the axial strain of a beam element should be... Therefore, an axial correction factor is introduced:

[0130]

[0131] Let the equation of the deflection curve of the plane beam be:

[0132] y=f(x) (34)

[0133] According to classical beam theory and mechanics of materials, the fundamental equation for calculating bending deformation is:

[0134]

[0135] Among them, curvature This indicates the degree of severe beam deformation; the greater the curvature, the more severe the deformation. M is the bending moment, and EI is called the beam's bending stiffness.

[0136] From the knowledge of differential calculus, the curvature expression of the torsion curve y = f(x) is:

[0137]

[0138] For the small elastic deformation of the beam, y'(x) = 1, [1+y' 2 (x)] 2 / 3 ≈1, therefore we can obtain

[0139]

[0140] Furthermore, the rotation angle of the beam can be approximated by the slope of the deflection curve:

[0141]

[0142] However, this approximation is unreasonable in structures undergoing large deformations, and it is impossible to calculate accurate results. Therefore, it is necessary to correct the approximation based on the actual relationship between bending moment and displacement during large deformations.

[0143] Based on equations (35), (36), and (38), a moment correction factor is introduced, which is used to correct the moment value by multiplying it by the corresponding moment:

[0144]

[0145] Where the coefficient α y and α z It is for M iy and M iz The correction, β y and β z It is for M jy and M jz The correction is as follows. Based on the internal force condition and equilibrium formula of the spatial beam element, we can obtain:

[0146]

[0147] Shear force is

[0148]

[0149] The shear force of the beam element after moment correction is:

[0150]

[0151] Based on equations (41) and (42), a shear force correction coefficient is introduced, which is:

[0152]

[0153] If the effect of large deformation curvature is approximately considered, the shear force correction factor can also be taken as:

[0154]

[0155] Based on the above formula, a large deformation correction matrix can be introduced into the calculation of large structural deformation.

[0156]

[0157] Therefore, equation (32) is modified according to the relationship between the actual internal forces and displacements in large deformations. Then, in the local coordinate system, the relationship between the element nodal forces and element nodal displacements is as follows:

[0158]

[0159] Where {f} is the element nodal force vector in the local coordinate system, and [k] e It is the elastic stiffness matrix of the spatial beam element. It is the element large deformation correction matrix. It is the element node displacement vector in the local coordinate system, {a} e [T] is the displacement vector of the unit node in the global coordinate system, and [T] is the coordinate transformation matrix.

[0160] In the global coordinate system, equation (46) can be written as:

[0161]

[0162] Where {F} is the element nodal force vector in the global coordinate system, and the element stiffness matrix in the global coordinate system for large structural deformation calculation is:

[0163]

[0164] Thus, the corrected element elastic stiffness matrix was obtained. Subsequently, a new structural stiffness equation was established based on the finite element method and Euler description, and a convergence criterion was set to iteratively calculate the equation, obtaining the displacement calculation results for large deformation of the truss structure.

[0165] In this embodiment, the convergence criterion is set as follows:

[0166]

[0167] Where {Δa} is the displacement difference vector, and ||{Δa}|| ∞ λ represents the maximum absolute value in the displacement difference vector, where λ is a very small number specified beforehand.

[0168] The process of establishing structural stiffness equations and iterative calculations is a standard procedure in this field, and will not be elaborated upon here to avoid obscuring the purpose of this application.

[0169] Based on the above-described large deformation structure calculation method, this embodiment provides a specific example to further illustrate the method of the present invention. For example... Figure 7 The diagram shows a cantilever beam model with the left end fixed and the right end free, subjected to a downward concentrated load F. Material parameters are set as follows: elastic modulus E = 79000 MPa, Poisson's ratio v = 0.3, beam length L = 1 m, circular cross-section with diameter d = 0.01 m, and cross-sectional area A = πd. 2 / 4=7.8540×10 -5 m 2 Moment of inertia I y =I z =πd 4 / 64=4.9087×10 -10 m4 Concentrated load F = 50 N.

[0170] The method of this invention is used for calculation and solution. The convergence condition is displacement control, requiring the maximum absolute value of the displacement difference vector to be less than 0.001m. In this example, the length of the cantilever beam remains unchanged before and after deformation. The solution results are as follows... Figure 8 As shown in the figure, the data displayed are the node coordinates (rounded to 4 decimal places).

[0171] Comparing the calculation results of the finite element analysis software MIDAS and the Euler algorithm (in this invention), it was found that the node with the maximum displacement was numbered 101, which is the rightmost node of the cantilever beam. Using MIDAS, the vertical displacement of the corresponding node was found to be -0.3687m, and the axial displacement was -0.0857m; using the Euler algorithm (in this invention), the vertical displacement of the corresponding node was found to be -0.3692m, and the axial displacement was -0.0869m. The results are very close.

[0172] This paper compares some key nodes in the Euler algorithm model (in this invention) and the MIDAS model. Since the model has 100 elements and 101 nodes, displaying all node data would be too dense, resulting in poor visual clarity and hindering observation. Therefore, in the cantilever beam model, one data point is selected every 5 nodes, for a total of 21 data points. Figure 9 The comparison results of the selected data points are shown. It is clear from the figure that the solution obtained by the Euler algorithm (this invention) is very close to, almost completely identical to, the solution obtained by the finite element analysis software MIDAS. This indicates that the Euler algorithm has high accuracy in handling this type of problem.

[0173] To clarify the universality of the solution method of this invention, the parameters of the model are modified, namely the dimensionless parameter λ = FL. 2 When / EI is 0.6, 0.8, 1.0, 1.2, and 1.4, F is 23.2674N, 31.0232N, 38.7790N, 46.5348N, and 54.2906N, respectively. The solutions were obtained using the method of this invention and the MIDAS software, and then compared with the exact solutions obtained using the elliptic integral method. The specific comparison results are shown in Table 1.

[0174] Table 1. Comparison of Euler's algorithm, MIDAS, and exact solutions for the cantilever beam model.

[0175]

[0176]

[0177] As shown in Table 1, in this cantilever beam model example, the results obtained using the Euler algorithm are highly accurate, with a maximum error of no more than 0.5% compared to the exact solution. The results obtained using the MIDAS algorithm are also basically consistent with those obtained using the Euler algorithm. Moreover, as the applied force increases, the deformation of the cantilever beam becomes larger, but the error does not increase significantly, meeting the required computational accuracy. After modifying the dimensionless parameters, the results obtained using the Euler algorithm and the MIDAS algorithm are compared... Figure 10 As shown.

[0178] As the load increases, the structural deformation will increase, and the number of iterations will also increase. However, the number of iterations in this method is still relatively small, less than the number of iterations required by the finite element analysis software MIDAS, and the program runs faster.

[0179] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for calculating large deformation of bar structures based on the Euler method, characterized in that, Includes the following steps: Step 1) Obtain the structural information to be analyzed and discretize it, dividing it into units; Step 2) Solve for the element elastic stiffness matrix of each element in the local coordinate system, and assemble them in the global coordinate system to obtain the global stiffness matrix; add boundary conditions and apply external forces to establish the structural stiffness equation, and solve for the global displacement and nodal displacement of the structure under small deformation conditions. Step 3) Establish the overall coordinate system and local coordinate system of the element and their relationship based on the position of the deformed structure, and determine the coordinate transformation matrix of the element; Step 4) Determine the large deformation correction matrix of the truss structure based on the relationship between the actual internal forces and displacements during large structural deformation, the differential equation of the beam's deflection curve, and the curvature formula. Step 5) Correct the elastic stiffness matrix of the element using the large deformation correction matrix and coordinate transformation matrix of the bar structure. Establish a new structural stiffness equation based on the finite element method and Euler description, and set a convergence criterion to iteratively calculate the equation to obtain the displacement calculation results of the large deformation of the bar structure.

2. The method for calculating large deformation of a rod structure based on the Euler method according to claim 1, characterized in that, The coordinate transformation matrix is: Where [T] is the coordinate transformation matrix and [t] is the node transformation matrix. These are the coordinate axes of the unit's local coordinate system established based on the position of the deformed structure.

3. The method for calculating large deformation of a rod structure based on the Euler method according to claim 1, characterized in that, The large deformation correction matrix for the rod structure is: in, V is the correction matrix for large deformation of the rod structure. N α is the axial correction factor. y α z β y β z γ is the bending moment correction factor. y γ z This is the shear force correction factor.

4. The method for calculating large deformation of a rod structure based on the Euler method according to claim 1, characterized in that, The calculation method for correcting the element elastic stiffness matrix using the large deformation correction matrix and coordinate transformation matrix of the bar structure is as follows: in, It is the large deformation correction matrix for the rod structure, [k]. e [T] is the elastic stiffness matrix of the spatial beam element, [K] is the coordinate transformation matrix, and [K] is the coordinate transformation matrix. e This is the corrected element elastic stiffness matrix.

5. The method for calculating large deformation of a rod structure based on the Euler method according to claim 1, characterized in that, The convergence criterion is as follows: Where {Δa} is the displacement difference vector, and ||{Δa}|| ∞ λ represents the maximum absolute value in the displacement difference vector, where λ is a very small number specified beforehand.

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