Static force calculation method for prefabricated dam

Abstract

A static force calculation method for a prefabricated dam is characterized in that a large number of joints in the prefabricated dam are simulated based on a finite element method and a contact element method, and attributes of contact elements are superposed into an integral stiffness matrix by using a traditional finite element integration rule; the overall stiffness matrix of the prefabricated dam is ensured to be a symmetric positive definite matrix, a linear equation set is solved by using Cholesky decomposition, and the iteration convergence speed is improved by using a preprocessing conjugate gradient method, so that the calculation efficiency is ensured. C # and FORTRAN programming language writing programs are used in a mixed mode to obtain a model information file and a contact unit information file, and heavy pretreatment work of fabricated dam performance analysis is completed; writing a program to convert a calculation result file into a post-processing file; except for the calculation efficiency of the method, the whole process of the method is almost completed through a program, and the performance analysis efficiency of the prefabricated dam is greatly improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of water conservancy engineering, and relates to a static calculation method for prefabricated and assembled dams. Background Art

[0002] Dams play roles in water resource management, river regulation, power generation and promoting economic development. For example, the Three Gorges Gravity Dam, the Baihetan Arch Dam, etc. The construction of dams is of great significance for developing rich water conservancy resources. The current widely used on-site casting construction method will produce a large amount of waste water and construction waste, and requires a large number of formworks. In addition, the quarrying of material yards will occupy a large amount of land and cause great damage to the landform landscape and vegetation. In addition, the cast-in-situ concrete construction requires strict temperature control measures to prevent cracks from appearing in the mass concrete during the cooling temperature drop process, which poses a potential safety hazard to the safe operation of the dam. On the contrary, the prefabricated and assembled construction technology avoids the above problems, greatly protects the local ecological environment, shortens the construction period, and is convenient for quality control, which is of great significance for the smooth completion of the dam.

[0003] There is extremely lack of design and construction experience for existing prefabricated and assembled dams. In the design process of prefabricated and assembled dams, it is necessary to quantitatively calculate the performance of prefabricated and assembled dams under various loads, including stress distribution and deformation. The finite element method is based on the finite element model of the dam and calculates its response under various load combinations, including displacement, stress distribution, and strain distribution.

[0004] The finite element method is widely used in various fields. This method discretizes the continuous solution domain into a combination of a finite number of elements, and such a combination can analytically simulate or approximate the solution region. An important step of the finite element method as a numerical analysis method is to use the approximate functions assumed in each element to represent the unknown field functions to be solved in the entire solution region. For prefabricated and assembled dams, there are a large number of mortar joints between precast blocks. The mortar joints, as weak layers in the assembled dams, will appear in states such as opening, sliding or closing under the action of loads. Commonly used finite element software such as Ansys, Abaqus, MSC.Marc, etc. are used to simulate this state of mortar joints by contact. Existing commercial finite element software calculates contact problems in the form of constraint inequalities. Commonly used algorithms include the penalty function method, the Lagrange multiplier method, the augmented Lagrange multiplier method, etc. These algorithms have poor generality when dealing with large-scale contact problems, and need to detect and identify contacts at each step of calculation, which requires a large amount of memory space and calculation time, and is not very suitable for engineering problems such as prefabricated and assembled dams where the contact positions are known in advance, which causes great difficulties for the design and popularization and application of prefabricated and assembled dams. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a static calculation method for precast assembled dams, which can quickly and accurately calculate the precast assembled dams, obtain the deformation and stress distribution of the precast assembled dams, and evaluate the mechanical properties of the precast assembled dams, including stiffness, maximum displacement and the most dangerous parts.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is: a static calculation method for precast assembled dams, comprising the following steps: S1. According to the design parameters of the precast assembled dam, establish a geometric model of the precast assembled dam in existing preprocessing software (Hypermesh, MarcMentat, Rhino), and specify material partitions, including cast-in-place concrete, precast concrete blocks, mortar, etc., to provide information for the subsequent identification of contact elements; S2. Further preprocessing work, write codes using C# and FORTRAN programming languages, process the model information file output by the preprocessing software, modify the model, delete invalid nodes and elements, re-number the elements and nodes, and output the model information file; S3. According to the material partitions specified in S1, identify the elements assigned with mortar material as contact elements. This work is completed using codes written in FORTRAN, automatically calculate the relevant information of the contact elements, and specify the attributes of the contact elements in this step, and output the contact element information file for the performance analysis of the precast assembled dam; S4. Write a calculation program combining the finite element method and the contact element method using FORTRAN language. The advantage of the contact element method is to use the traditional finite element integration rule to superimpose the attributes of the contact elements into the global stiffness matrix to ensure that the global stiffness matrix of the precast assembled dam is a symmetric positive definite matrix, and use Cholesky decomposition to solve the linear equations; S5. Import the model information file output in S2 and the contact element information file output in S3 into the calculation program developed in S4, and input loads according to different working conditions, and calculate the responses of the precast assembled dam under different load combinations; S6. Output the calculation results in S5. The output results are binary files, and use FORTRAN codes to convert them into specific formats recognized by post-processing software Tecplot and GiD, input them into the post-processing software to visualize the calculation results, quantitatively analyze the displacement and stress distribution of the precast assembled dam, and determine the performance of the precast assembled dam.

[0007] In S3, there are 8 nodes in the contact element, each node has 3 degrees of freedom, and there are a total of 24 degrees of freedom. x 、 y 、 z are the global coordinate systems.η, ξ, ζ is the local coordinate system, let be the displacements of each node of the contact element in the local coordinate system, be the displacements of each node of the element in the global coordinate system, and the relationship between the two is:

[0008] In the formula, is the transformation matrix; the average relative displacement of the upper and lower surfaces of the contact element can be expressed as:

[0009] In the formula, is the shape function matrix; is the displacement vector of the element in the global coordinate system.

[0010] In S3, according to the principle of virtual work, the global stiffness matrix of the contact element is derived as:

[0011] In the formula, a is the area of the contact element; is the elastic matrix of the contact element; the elastic matrix of the contact element The calculation formula is:

[0012] In the formula, and are the tangential stiffnesses in two directions of the contact element; is the normal stiffness of the contact element.

[0013] In S3, the elastic matrix of the contact element is closely related to its contact state, i.e., closed, sliding, and open, and the calculation formula is:

[0014] In the formula, and are the tangential stiffnesses of the contact element; is the normal stiffness of the contact element; f and c are the friction coefficient and cohesion of the contact element; and The tangential stress components in two directions of the contact element; is the normal stress component, i.e., negative for compression and positive for tension; is the initial gap between the contact element and the adjacent element surface.

[0015] In S3, the normal and tangential stresses of the contact element are calculated according to the following formula:

[0016] After obtaining the element stiffness matrix of the contact element, the stiffness of the contact element is integrated into the overall stiffness matrix of the model through the finite element stiffness integration rule to obtain the overall stiffness matrix of the model, and the displacements of each node of the model are calculated by the following formula:

[0017] In the formula, represents the overall stiffness matrix of the model; is the nodal displacement vector in the model; is the nodal load vector.

[0018] In S3, during the static calculation of the assembled dam, the contact state of the contact elements in the assembled dam needs to be determined through iterative calculation. The iterative format for determining the contact state of the contact elements is:

[0019] Where: is the overall stiffness matrix at the i -1 step, which changes with the contact state;

[0020] In the formula, is the set of joint surface elements whose contact state changes between two consecutive iterations;

[0021] In the formula: is the stress increment of the contact element under the condition that the contact state is assumed not to change in the i th iteration; is the stress increment in the i th iteration. From the i- 1st iteration to the i th iteration, if the contact state remains unchanged, then = ; otherwise:

[0022] In each iteration, the contact state of the contact element is determined according to the calculated average relative displacement of the nodes, the incremental average relative displacement, and the stress components calculated based on the assumed contact state, and the stress increment of the contact element with the changed contact state is calculated according to Equation 15.

[0023] In S6, a large number of joints in the precast assembled dam are simulated based on the finite element method and the contact element method. Using the traditional finite element integration rule, the properties of the contact elements are superimposed into the global stiffness matrix to ensure that the global stiffness matrix of the precast assembled dam is a symmetric positive definite matrix. The linear equations are solved using the Cholesky decomposition, and the preconditioned conjugate gradient method is used to improve the iterative convergence speed to ensure the calculation efficiency.

[0024] The main beneficial effects of the present invention are as follows: A program is written in a programming language to obtain the model information file and the contact element information file, completing the heavy preprocessing work of the performance analysis of the assembled dam; and a program is written to convert the calculation result file into a postprocessing file; except for the calculation efficiency of the method of the present invention itself, almost the whole process of the present invention is completed by programs, greatly improving the performance analysis efficiency of the precast assembled dam.

[0025] Adopting the performance analysis method of the precast assembled dam provided by the present invention, the performance of the precast assembled dam is quantitatively evaluated, and the deformation and stress distribution of the precast assembled dam under various load combinations are evaluated, providing a basic technical support for the design and application of the precast assembled dam. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] The present invention will be further described below with reference to the drawings and embodiments.

[0027] Figure 1 is a flow chart of the present invention.

[0028] Figure 2 is a schematic diagram of the material zoning of the assembled dam of the present invention.

[0029] Figure 3 is a contact element diagram of the present invention.

[0030] Figure 4 is an information diagram included in the contact element of the present invention.

[0031] Figure 5 is a displacement distribution diagram of a certain precast assembled dam in a specific embodiment of the present invention.

[0032] Figure 6 is a stress distribution diagram of a certain precast assembled dam in a specific embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] As Figures 1 to 6 in, a static calculation method for a precast assembled dam includes the following steps: S1. According to the design parameters of the prefabricated and assembled dam, establish the geometric model of the prefabricated and assembled dam in the existing preprocessing software (Hypermesh, MarcMentat, Rhino), and specify the material partitions, including cast-in-place concrete, precast concrete blocks, mortar, etc., to provide information for the subsequent identification of contact elements; S2. For further preprocessing work, write code using C# and FORTRAN programming languages to process the model information file output by the preprocessing software, correct the model, delete invalid nodes and elements, renumber the elements and nodes, and output the model information file; S3. According to the material partitions specified in S1, identify the elements assigned with mortar material as contact elements. This work is completed using the code written in FORTRAN, automatically calculate the relevant information of the contact elements, and specify the attributes of the contact elements in this step, and output the contact element information file for the performance analysis of the prefabricated and assembled dam; S4. Write a calculation program combining the finite element method and the contact element method using FORTRAN language. The advantage of the contact element method is to use the traditional finite element integration rule to superimpose the attributes of the contact elements into the global stiffness matrix to ensure that the global stiffness matrix of the prefabricated and assembled dam is a symmetric positive definite matrix, and use Cholesky decomposition to solve the linear equations; S5. Import the model information file output in S2 and the contact element information file output in S3 into the calculation program developed in S4, and input the loads according to different working conditions to calculate the responses of the prefabricated and assembled dam under different load combinations; S6. Output the calculation results in S5. The output results are binary files, and use FORTRAN code to convert them into specific formats recognized by the post-processing software Tecplot and GiD, input them into the post-processing software to visualize the calculation results, quantitatively analyze the displacement and stress distribution of the prefabricated and assembled dam, and determine the performance of the prefabricated and assembled dam.

[0034] Example 1 The performance analysis process of the prefabricated and assembled dam based on the finite element method and the contact element method is as Figure 1 shown. The specific steps are as follows: (1) According to the structural design parameters, use the Mentat preprocessing module of Marc finite element software to establish a geometric model, divide it using 8-node hexahedron meshes, and specify the material partitions, including cast-in-place concrete, precast concrete blocks, impervious panels, gate piers, mortar joints, etc. Figure 2 shows the schematic diagram of the material partition of a numerical model of a prefabricated and assembled dam; (2) Further preprocessing work is carried out. Codes are written using C# and FORTRAN programming languages to process the model information file output from the preprocessing software, correct the model, delete invalid nodes and elements, re-number the elements and nodes, and output the model information file. The model information file includes: the number of nodes, node numbers, node coordinates, the number of elements, element numbers, the node numbers forming the element, and the element material numbers; (3) According to the material partition specified in step (1), the elements assigned with mortar material are identified as contact elements. The contact elements are as shown in Figure 3 . There are 8 nodes in each contact element, each node has 3 degrees of freedom, and there are a total of 24 degrees of freedom. Figure 3 In x , y , z is the global coordinate system, η, ξ, ζ is the local coordinate system. Let be the displacements of each node of the contact element in the local coordinate system, be the displacements of each node of the element in the global coordinate system. The relationship between the two is:

[0035] where: is the transformation matrix. The average relative displacement of the upper and lower surfaces of the contact element can be expressed as:

[0036] In the formula, is the shape function matrix; is the displacement vector of the element in the global coordinate system. According to the principle of virtual work, the global stiffness matrix of the contact element is deduced as:

[0037] In the formula, a is the area of the contact element; is the elastic matrix of the contact element. The elastic matrix of the contact element is calculated as:

[0038] In the formula, and are the tangential stiffnesses in two directions of the contact element; is the normal stiffness of the contact element. The elastic matrix of the contact element is closely related to its contact state (closed, sliding, and open), and the calculation formula is:

[0039] In the formula, and are the tangential stiffnesses of the contact element; is the normal stiffness of the contact element; f and c are the friction coefficient and cohesion of the contact element; and are the tangential stress components in two directions of the contact element; is the normal stress component (negative for compression and positive for tension); is the initial gap between the contact element and the adjacent element surface. The stresses in the normal and tangential directions of the contact element are calculated as follows:

[0040] After obtaining the element stiffness matrix of the contact element, through the finite element stiffness integration rule, the stiffness of the contact element is integrated into the overall stiffness matrix of the model to obtain the overall stiffness matrix of the model, and the displacements of each node of the model are calculated by the following formula:

[0041] where represents the overall stiffness matrix of the model; is the node displacement vector in the model; is the node load vector. In the process of static calculation of the assembled dam, the contact state of the contact element in the assembled dam needs to be determined by iterative calculation. The iterative format for determining the contact state of the contact element is:

[0042] where: is the overall stiffness matrix at the i -1 step, which changes with the contact state;

[0043] where is the set of joint surface elements whose contact state changes between two consecutive iterations;

[0044] where: is the stress increment of the contact element under the condition that the contact state is assumed not to change at the i th iteration; is the stress increment at the i th iteration. From the i- 1st iteration to the i th iteration, if the contact state remains unchanged, then = ; otherwise:

[0045] In each iteration, the contact state of the contact elements is determined based on the average relative displacement of the calculation nodes, the incremental average relative displacement, and the stress components calculated from the assumed contact state, and the stress increment of the contact elements with changed contact state is calculated according to Equation 15.

[0046] The identification of contact elements is completed using the code written in FORTRAN, and the relevant information of contact elements is automatically calculated. The information diagram of contact elements is shown as Figure 4 follows, including: the number of contact elements in the overall model, the adjacent elements of contact elements, the face number of contact elements as the contact surface, etc. And the properties of contact elements are specified in this step, including the cohesion, friction coefficient and tensile strength of contact elements, and the contact element information file is output for the performance analysis of precast assembled dams; (4) The combined finite element method and contact element method use FORTRAN language to write the structural calculation program for precast assembled dams. The advantage of the contact element method is to use the traditional finite element integration rule to superimpose the properties of contact elements into the overall stiffness matrix to ensure that the overall stiffness matrix of precast assembled dams is symmetric positive definite, and the Cholesky decomposition is used to solve the linear equations; when calculating each load step, since the state of contact elements is unknown (closed, sliding or open), it is necessary to iterate continuously until the state of contact elements does not change. The preconditioned conjugate gradient iteration algorithm is used in the iteration process to accelerate the iteration process and improve the calculation efficiency of the calculation program.

[0047] (5) Import the model information file output in step (2) and the contact element information file output in step (3) into the calculation program developed in step (4), and consider different working condition combinations, including: upstream water level, structural self-weight, gantry load, downstream water level, etc., and input loads according to design requirements to calculate the responses of precast assembled dams under different load combinations; (6) Output the calculation results in step (5), save the results as binary files. Binary files save hard disk space. Use FORTRAN to write code, and this code converts the output binary files into the file format recognized by the post-processing software, and then inputs them into the post-processing software to visualize the calculation results. For example, Figure 5 and Figure 6 are respectively the displacement distribution (unit: m) and stress distribution (unit: MPa) of a specific precast assembled dam under the action of hydrostatic pressure and gravity. It can be seen that the maximum displacement of the assembled dam occurs at the downstream dam crest, about 1.745 mm. The displacement and stress distributions of the precast assembled dam are quantitatively analyzed through the calculation results to determine the performance of the precast assembled dam.

[0048] Based on the finite element method and the contact element method, a large number of joints in the prefabricated dam are simulated. Using the traditional finite element integration rule, the properties of the contact elements are superimposed into the global stiffness matrix to ensure that the global stiffness matrix of the prefabricated dam is a symmetric positive definite matrix. The Cholesky decomposition is used to solve the linear equations, and the preconditioned conjugate gradient method is used to improve the iterative convergence speed, thereby ensuring the calculation efficiency.

[0049] Programs are written in a programming language to obtain the model information file and the contact element information file, completing the heavy preprocessing work for the performance analysis of the prefabricated dam; and programs are written to convert the calculation result file into a postprocessing file. Except for the calculation efficiency of the method of the present invention itself, almost the entire process of the present invention is completed through programs, greatly improving the performance analysis efficiency of the prefabricated dam.

[0050] Adopting the prefabricated dam performance analysis method provided by the present invention, the performance of the prefabricated dam is quantitatively evaluated, and the deformation and stress distribution of the prefabricated dam under various load combinations are evaluated, providing a basic technical support for the design and application of the prefabricated dam.

[0051] The above embodiments are only the preferred technical solutions of the present invention and should not be regarded as limitations on the present invention. The embodiments in this application and the features in the embodiments can be arbitrarily combined with each other without conflict. The protection scope of the present invention should be the technical solutions recorded in the claims, including the equivalent replacement solutions of the technical features in the technical solutions recorded in the claims. That is, the equivalent replacement improvements within this scope are also within the protection scope of the present invention.

Claims

1. A static calculation method for prefabricated assembled dams, characterized in that: The steps include: S1. According to the design parameters of the prefabricated dam, the geometric model of the prefabricated dam is established in the existing pre-processing software (Hypermesh, Marc Mentat, Rhino), and the material partitions are specified, including cast-in-place concrete, prefabricated concrete blocks, mortar, etc., to provide information for the subsequent identification of contact elements; S2, further pre-processing work, using C# and FORTRAN programming languages ​​to write codes, process the model information file output from the pre-processing software, modify the model, delete invalid nodes and units, renumber units and nodes, and output the model information file; S3, according to the material partition specified in S1, the unit assigned to the mortar material is identified as a contact unit. This work is completed using a code written in FORTRAN, and the relevant information of the contact unit is automatically calculated. In this step, the properties of the contact unit are specified, and the contact unit information file is output for the performance analysis of the prefabricated assembled dam; S4, use FORTRAN language to write a calculation program combining finite element method and contact element method. The advantage of contact element method is that it uses the traditional finite element integration rules to superimpose the properties of the contact element into the overall stiffness matrix, ensuring that the overall stiffness matrix of the prefabricated dam is a symmetric positive definite matrix, and uses Cholesky decomposition to solve the linear equations; S5, importing the model information file outputted in S2 and the contact unit information file outputted in S3 into the calculation program developed in S4, and inputting loads according to different working conditions to calculate the response of the prefabricated assembled dam under different load combinations; S6, output the calculation results in S5, the output results are binary files, and use FORTRAN code to convert them into a specific format recognized by post-processing software Tecplot and GiD, input the visualization calculation results into the post-processing software, quantitatively analyze the displacement and stress distribution of the prefabricated assembled dam, and determine the performance of the prefabricated assembled dam.

2. The static calculation method for prefabricated assembled dam according to claim 1 is characterized by: In S3, there are 8 nodes in the contact element, each node has 3 degrees of freedom, a total of 24 degrees of freedom. x , y , z is the global coordinate system, η, ξ, ζ is the local coordinate system, let is the displacement of each node of the contact element in the local coordinate system, is the displacement of each node of the unit in the global coordinate system, and the relationship between the two is: In the formula, is the transformation matrix; the average relative displacement of the upper and lower sides of the contact unit can be expressed as: In the formula, is the shape function matrix; is the element global coordinate system displacement vector.

3. The static calculation method for prefabricated assembled dam according to claim 2 is characterized by: In S3, the global stiffness matrix of the contact element is derived according to the virtual work principle: In the formula, a is the area of ​​the contact unit; is the elastic matrix of the contact element.

4. The static calculation method for prefabricated assembled dam according to claim 3 is characterized by: Elasticity Matrix of Contact Elements The calculation formula is: In the formula, and is the tangential stiffness of the contact element in both directions; is the normal stiffness of the contact element.

5. The static calculation method for prefabricated assembled dam according to claim 4 is characterized by: In S3, the elastic matrix of the contact element is closely related to its contact state, namely, closed, slipped, and opened, and the calculation formula is: In the formula, and is the tangential stiffness of the contact element; is the normal stiffness of the contact element; f and c are the friction coefficient and cohesion of the contact element; and The tangential stress components of the contact element in two directions; is the normal stress component, i.e. negative for compression and positive for tension; is the initial gap between the contact element and the adjacent element surface.

6. The static calculation method for prefabricated assembled dam according to claim 5 is characterized by: In S3, the stress in the normal and tangential directions of the contact element is calculated according to the following formula: 。 7. The static calculation method for prefabricated assembled dam according to claim 6 is characterized by: In S3, after obtaining the unit stiffness matrix of the contact unit, the stiffness of the contact unit is integrated into the overall stiffness matrix of the model through the finite element stiffness integration rule to obtain the overall stiffness matrix of the model, and the displacement of each node of the model is calculated by the following formula: In the formula, Represents the global stiffness matrix of the model; is the node displacement vector in the model; is the node load vector.

8. The static calculation method for prefabricated assembled dam according to claim 3 is characterized by: In S3, during the static calculation of the prefabricated dam, the contact state of the contact unit in the prefabricated dam needs to be determined through iterative calculation. The iterative format for determining the contact state of the contact unit is: in: For the i -1 step global stiffness matrix, which changes as the contact state changes; In the formula, is the set of seam surface elements whose contact status changes between the previous and next iterations; Where: For the i The stress increment of the contact element under the condition that the contact state does not change in the iteration; For the i The stress increment of the iteration is i- 1 iteration to the i In iterations, if the contact state does not change, then = ;otherwise: 。 9. The static calculation method for prefabricated assembled dam according to claim 8 is characterized in that: In each iteration, the contact state of the contact unit is determined based on the calculated node average relative displacement, incremental average relative displacement, and stress components calculated based on the assumed contact state, and the stress increment of the contact unit with changed contact state is calculated according to Equation (15).

10. The static calculation method for prefabricated assembled dam according to claim 1 is characterized in that: In S6, a large number of joints in the prefabricated dam are simulated based on the finite element method and the contact element method. The properties of the contact element are superimposed on the overall stiffness matrix using the traditional finite element integration rule to ensure that the overall stiffness matrix of the prefabricated dam is a symmetric positive definite matrix. The Cholesky decomposition is used to solve the linear equations, and the preconditioned conjugate gradient method is used to improve the iterative convergence speed and ensure the computational efficiency.

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