Static calculation method for precast dam

Abstract

A kind of static calculation method for prefabricated dam, based on finite element method and contact element method, a large number of joints in prefabricated dam are simulated, the properties of contact element are superimposed into the overall stiffness matrix using traditional finite element integration rule, to ensure that the overall stiffness matrix of prefabricated dam is a symmetric positive definite matrix, the linear equations are solved using Cholesky decomposition, and the iterative convergence speed is improved using preconditioned conjugate gradient method, to ensure the calculation efficiency. C# and FORTRAN programming language are used to write programs to obtain model information file and contact element information file, to complete the heavy pre-processing work of prefabricated dam performance analysis, and programs are written to convert the calculation result file into post-processing file; in addition to the calculation efficiency of the method itself, the whole process of the application is almost completed by program, which greatly improves the performance analysis efficiency of prefabricated dam.

Description

Technical Field

[0001] This invention belongs to the field of water conservancy engineering technology and relates to a static calculation method for prefabricated assembled dams. Background Technology

[0002] Dams play a crucial role in water resource management, river control, power generation, and economic development. Examples include the Three Gorges Gravity Dam and the Baihetan Arch Dam. The construction of dams is of great significance for developing abundant water resources. Currently, cast-in-place construction is widely used. This method generates large amounts of wastewater and construction debris, requires extensive formwork, and quarries occupy significant land, causing substantial damage to the landscape and vegetation. Furthermore, cast-in-place concrete construction requires strict temperature control to prevent cracks from forming in large volumes of concrete during cooling, which could jeopardize the dam's safe operation. In contrast, precast assembly construction avoids these problems, greatly protects the local ecological environment, shortens the construction period, and facilitates quality control, making it of great importance for the successful completion of dams.

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

[0004] The finite element method (FEM) is widely used in various fields. This method discretizes the continuous solution domain into a finite set of elements, which analytically simulates or approximates the solution domain. A key step in the FEM as a numerical analysis method is to represent the unknown field function to be solved over the entire solution domain using an approximate function assumed within each element. For precast dams, there are numerous mortar joints between the precast blocks. These mortar joints, acting as weak layers in the dam, can open, slip, or close under load. Commonly used finite element software such as Ansys, Abaqus, and MSC.Marc uses contact simulation to model these states of the mortar joints. Existing commercial finite element software calculates contact problems using constraint inequalities. Commonly used algorithms include the penalty function method, the Lagrange multiplier method, and the augmented Lagrange multiplier method. These algorithms have poor versatility when dealing with large-scale contact problems, and they require contact detection and identification at each step of the calculation, which consumes a lot of memory space and computation time. They are not suitable for engineering problems such as prefabricated dams where the contact positions are known in advance. This has caused great difficulties for the design and promotion of prefabricated dams. Summary of the Invention

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

[0006] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a static calculation method for prefabricated assembled dams, comprising the following steps:

[0007] S1. Based on the design parameters of the prefabricated dam, a geometric model of the prefabricated dam is established in the existing pre-processing software (Hypermesh, MarcMentat, Rhino), and material partitions are specified, including cast-in-place concrete, prefabricated concrete blocks, mortar, etc., to provide information for the subsequent identification of contact units.

[0008] S2, further preprocessing work, using C# and FORTRAN programming languages ​​to write code 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;

[0009] S3, based on the material partition specified in S1, identifies the elements assigned to the mortar material as contact elements. This work is completed using code written in FORTRAN, automatically calculates the relevant information of the contact elements, specifies the properties of the contact elements in this step, and outputs the contact element information file for the performance analysis of prefabricated assembled dams.

[0010] S4. The calculation program for the combined finite element method and the contact element method is written in FORTRAN language. The advantage of the contact element method is that it uses the traditional finite element integration rules to superimpose the properties of the contact elements into the overall stiffness matrix, ensuring that the overall stiffness matrix of the prefabricated dam is a symmetric positive definite matrix. The linear equation system is solved using Cholesky decomposition.

[0011] S5 imports the model information file output from S2 and the contact element information file output from S3 into the calculation program developed in S4, and calculates the response of the prefabricated dam under different load combinations based on the input loads under different working conditions.

[0012] S6 outputs the calculation results from S5. The output results are in binary format. The FORTRAN code is used to convert them into a specific format that can be recognized by the post-processing software Tecplot and GiD. The results are then input into the post-processing software to visualize the calculation results, quantitatively analyze the displacement and stress distribution of the prefabricated dam, and determine the performance of the prefabricated dam.

[0013] In S3, the contact element has 8 nodes, each node has 3 degrees of freedom, for a total of 24 degrees of freedom. x , y , z Using the global coordinate system, η, ξ, ζ Let be a local coordinate system. Let represent the displacement of each node of the contact element in the local coordinate system. Let $\mathbf$ be the displacement of each node in the element in the global coordinate system, and the relationship between the two is as follows:

[0014]

[0015] In the formula, The transformation matrix is ​​given; the average relative displacement between the upper and lower surfaces of the contact element can be expressed as:

[0016]

[0017] In the formula, It is a matrix of shape functions; It is the displacement vector of the unit's global coordinate system.

[0018] In S3, the global stiffness matrix of the contact element is derived based on the principle of virtual work as follows:

[0019]

[0020] In the formula, a The area of ​​the contact unit; Here is the elasticity matrix of the contact element; The calculation formula is:

[0021]

[0022] In the formula, and It refers to the tangential stiffness of the contact element in two directions; It is the normal stiffness of the contact element.

[0023] In S3, the elastic matrix of the contact element is closely related to its contact state, namely closed, sliding, and open, and the calculation formula is as follows:

[0024]

[0025] In the formula, and It is the tangential stiffness of the contact element; It is the normal stiffness of the contact element; f and c These are the friction coefficient and cohesion of the contact unit; and Tangential stress components in two directions of the contact element; It is the normal stress component, that is, negative under compression and positive under tension; It is the initial gap between the contact element and the adjacent element surface.

[0026] In S3, the stresses in the normal and tangential directions of the contact element are calculated according to the following formula:

[0027]

[0028] After obtaining the element stiffness matrix of the contact element, the stiffness of the contact element is integrated into the overall model stiffness matrix using the finite element stiffness integration rule to obtain the overall model stiffness matrix. The displacement of each node in the model is then calculated using the following formula:

[0029]

[0030] In the formula, The overall stiffness matrix of the model; This refers to the nodal displacement vectors in the model; This represents the nodal load vector.

[0031] In S3, during the static calculation of prefabricated dams, the contact state of contact elements in the prefabricated dam needs to be determined through iterative calculation. The iterative format for determining the contact state of contact elements is as follows:

[0032]

[0033] in: For the first i The overall stiffness matrix of step -1 changes with the contact state;

[0034]

[0035] In the formula, This is the set of seam units whose contact state changes between the two iterations;

[0036]

[0037] In the formula: For the first i The stress increment of the contact element under the assumption that the contact state does not change in the next iteration; For the first i The stress increment of the iteration, from the first iteration i- 1st iteration to the 1st i In the next iteration, if the contact state remains unchanged, then = ;otherwise:

[0038]

[0039] In each iteration, the contact state of the contact element is determined based on the average relative displacement of the calculated nodes, the incremental average relative displacement, and the stress components calculated under the assumed contact state. The stress increment of the contact element due to the change in contact state is calculated according to Equation 14.

[0040] In S6, a large number of joints in prefabricated dams are simulated based on the finite element method and the contact element method. The traditional finite element integration rule is used to superimpose the properties of the contact elements into the overall stiffness matrix 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 equation system, and the preprocessing conjugate gradient method is used to improve the iteration convergence speed and ensure computational efficiency.

[0041] The main beneficial effects of this invention are as follows:

[0042] The invention uses programming languages ​​to write programs to obtain model information files and contact element information files, completing the arduous preprocessing work for the performance analysis of prefabricated dams; and writes programs to convert the calculation result files into post-processing files; apart from the computational efficiency of the method itself, the entire process of the invention is almost entirely completed by programs, greatly improving the efficiency of performance analysis of prefabricated dams.

[0043] The performance analysis method for prefabricated assembled dams provided by this invention is used to quantitatively evaluate the performance of prefabricated assembled dams, assess the deformation and stress distribution of prefabricated assembled dams under various load combinations, and provide basic technical support for the design and application of prefabricated assembled dams. Attached Figure Description

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] Figure 1 This is a flowchart of the present invention.

[0046] Figure 2 This is a schematic diagram of the material zoning for the prefabricated dam of the present invention.

[0047] Figure 3 This is a diagram of the contact unit of the present invention.

[0048] Figure 4 This is an information diagram of the contact unit of the present invention.

[0049] Figure 5 This is a displacement distribution diagram of a prefabricated assembled dam according to a specific embodiment of the present invention.

[0050] Figure 6 This is a stress distribution diagram of a prefabricated assembled dam according to a specific embodiment of the present invention. Detailed Implementation

[0051] like Figures 1-6 A static calculation method for prefabricated assembled dams includes the following steps:

[0052] S1. Based on the design parameters of the prefabricated dam, a geometric model of the prefabricated dam is established in the existing pre-processing software (Hypermesh, MarcMentat, Rhino), and material partitions are specified, including cast-in-place concrete, prefabricated concrete blocks, mortar, etc., to provide information for the subsequent identification of contact units.

[0053] S2, further preprocessing work, using C# and FORTRAN programming languages ​​to write code 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;

[0054] S3, based on the material partition specified in S1, identifies the elements assigned to the mortar material as contact elements. This work is completed using code written in FORTRAN, automatically calculates the relevant information of the contact elements, specifies the properties of the contact elements in this step, and outputs the contact element information file for the performance analysis of prefabricated assembled dams.

[0055] S4. The calculation program for the combined finite element method and the contact element method is written in FORTRAN language. The advantage of the contact element method is that it uses the traditional finite element integration rules to superimpose the properties of the contact elements into the overall stiffness matrix, ensuring that the overall stiffness matrix of the prefabricated dam is a symmetric positive definite matrix. The linear equation system is solved using Cholesky decomposition.

[0056] S5 imports the model information file output from S2 and the contact element information file output from S3 into the calculation program developed in S4, and calculates the response of the prefabricated dam under different load combinations based on the input loads under different working conditions.

[0057] S6 outputs the calculation results from S5. The output results are in binary format. The FORTRAN code is used to convert them into a specific format that can be recognized by the post-processing software Tecplot and GiD. The results are then input into the post-processing software to visualize the calculation results, quantitatively analyze the displacement and stress distribution of the prefabricated dam, and determine the performance of the prefabricated dam.

[0058] Example 1,

[0059] The performance analysis process for prefabricated assembled dams based on the finite element method and contact element method is as follows: Figure 1 As shown, the specific steps are as follows:

[0060] (1) Based on the structural design parameters, the geometric model was established using the Mentat preprocessing module of the Marc finite element software. An 8-node hexahedral mesh was used for meshing, and material partitions were defined, including cast-in-place concrete, precast concrete blocks, anti-seepage panels, gate piers, mortar joints, etc. Figure 2 A schematic diagram of material partitioning for a numerical model of a prefabricated dam is shown.

[0061] (2) Further preprocessing work is carried out. The model information file output by the preprocessing software is processed using C# and FORTRAN programming languages. The model is corrected, invalid nodes and elements are deleted, and the elements and nodes are renumbered. The model information file is output, which includes: number of nodes, node number, node coordinates, number of elements, element number, number of constituent element nodes, and element material number.

[0062] (3) Based on the material partition specified in step (1), the unit to which the mortar material is applied is identified as a contact unit, such as... Figure 3 As shown, the contact element has 8 nodes, each node has 3 degrees of freedom, for a total of 24 degrees of freedom. Figure 3 In x , y , z Using the global coordinate system, η, ξ, ζ Let be a local coordinate system. Let represent the displacement of each node of the contact element in the local coordinate system. Let $\mathbf$ be the displacement of each node in the element in the global coordinate system, and the relationship between the two is as follows:

[0063]

[0064] in: Here is the transformation matrix. The average relative displacement between the upper and lower surfaces of the contact element can be expressed as:

[0065]

[0066] In the formula, It is a matrix of shape functions; This is the displacement vector in the global coordinate system of the element. Based on the principle of virtual work, the global stiffness matrix of the contact element is derived as follows:

[0067]

[0068] In the formula, a The area of ​​the contact unit; This is the elasticity matrix of the contact element. The calculation formula is:

[0069]

[0070] In the formula, and It refers to the tangential stiffness of the contact element in two directions; This refers to 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:

[0071]

[0072] In the formula, and It is the tangential stiffness of the contact element; It is the normal stiffness of the contact element; f and c These are the friction coefficient and cohesion of the contact unit; and Tangential stress components in two directions of the contact element; It is the normal stress component (negative under compression, positive under tension). This is the initial gap between the contact element and the adjacent element surface. The stress in the normal and tangential directions of the contact element is calculated according to the following formula:

[0073]

[0074] After obtaining the element stiffness matrix of the contact element, the stiffness of the contact element is integrated into the overall model stiffness matrix using the finite element stiffness integration rule to obtain the overall model stiffness matrix. The displacement of each node in the model is then calculated using the following formula:

[0075]

[0076] In the formula, The overall stiffness matrix of the model; This refers to the nodal displacement vectors in the model; This represents the nodal load vector. In the static calculation of prefabricated dams, the contact state of contact elements needs to be determined through iterative calculation. The iterative format for determining the contact state of contact elements is as follows:

[0077]

[0078] in: For the first i The overall stiffness matrix of step -1 changes with the contact state;

[0079]

[0080] In the formula, This is the set of seam units whose contact state changes between the two iterations;

[0081]

[0082] In the formula: For the first i The stress increment of the contact element under the assumption that the contact state does not change in the next iteration; For the first i The stress increment of the iteration, from the first iteration i- 1st iteration to the 1st i In the next iteration, if the contact state remains unchanged, then = ;otherwise:

[0083]

[0084] In each iteration, the contact state of the contact element is determined based on the average relative displacement of the calculated nodes, the incremental average relative displacement, and the stress components calculated under the assumed contact state. The stress increment of the contact element due to the change in contact state is calculated according to Equation 14.

[0085] The identification of contact elements was accomplished using code written in FORTRAN, which automatically calculated relevant information for each contact element. The contact element information is illustrated in the diagram below. Figure 4 As shown, this includes: the contact element's number in the overall model, the contact element's adjacent elements, and the face number of the contact element as a contact surface. This step also specifies the contact element's properties, including its cohesion, coefficient of friction, and tensile strength, and outputs a contact element information file for performance analysis of prefabricated dams.

[0086] (4) The structural calculation program for prefabricated dams was written using FORTRAN language, combining the finite element method and the contact element method. The advantage of the contact element method is that it uses the traditional finite element integration rules to superimpose the properties of the contact elements into the overall stiffness matrix, ensuring that the overall stiffness matrix of the prefabricated dam is a symmetric positive definite matrix. The linear equation system is solved using Cholesky decomposition. When calculating each load step, since the state of the contact elements is unknown (closed, slipped or open), it is necessary to iterate continuously until the state of the contact elements does not change. The iteration process adopts the preprocessing conjugate gradient iteration algorithm to accelerate the iteration process and improve the calculation efficiency of the calculation program.

[0087] (5) Import the model information file output in step (2) and the contact unit information file output in step (3) into the calculation program developed in step (4), and consider different combinations of working conditions, including: upstream water level, structural self-weight, gantry crane load, downstream water level, etc., and input the load according to the design requirements to calculate the response of the prefabricated dam under different load combinations.

[0088] (6) Output the calculation results in step (5) and save the results as a binary file. Binary files save hard disk space. Use FORTRAN to write code that converts the output binary file into a file format that the post-processing software can recognize. Then input the result into the post-processing software to visualize the calculation results, such as... Figure 5 and Figure 6 The figures show the displacement (in meters) and stress (in MPa) distribution of a prefabricated dam under the combined action of hydrostatic pressure and gravity in a specific embodiment. It can be seen that the maximum displacement of the prefabricated dam occurs at the downstream dam crest, which is about 1.745 mm. The displacement and stress distribution of the prefabricated dam are quantitatively analyzed through calculation results to determine the performance of the prefabricated dam.

[0089] The numerous joints in prefabricated dams are simulated using the finite element method and the contact element method. The traditional finite element integration rule is used to superimpose the properties of the contact elements into the overall stiffness matrix, ensuring that the overall stiffness matrix of the prefabricated dam is a symmetric positive definite matrix. The linear equation system is solved using Cholesky decomposition, and the preprocessed conjugate gradient method is used to improve the iteration convergence speed, thereby ensuring computational efficiency.

[0090] The invention uses programming languages ​​to write programs to obtain model information files and contact element information files, completing the arduous preprocessing work for the performance analysis of prefabricated dams; and writes programs to convert the calculation result files into post-processing files; apart from the computational efficiency of the method itself, the entire process of the invention is almost entirely completed by programs, greatly improving the efficiency of performance analysis of prefabricated dams.

[0091] The performance analysis method for prefabricated assembled dams provided by this invention is used to quantitatively evaluate the performance of prefabricated assembled dams, assess the deformation and stress distribution of prefabricated assembled dams under various load combinations, and provide basic technical support for the design and application of prefabricated assembled dams.

[0092] The above embodiments are merely preferred technical solutions of the present invention and should not be considered as limitations on the present invention. The embodiments and features described in these embodiments can be combined arbitrarily without conflict. The scope of protection of the present invention should be limited to the technical solutions described in the claims, including equivalent substitutions of the technical features described in the claims. That is, equivalent substitutions and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A static calculation method for prefabricated assembled dams, characterized in that, Includes the following steps: S1. Based on the design parameters of the prefabricated dam, a geometric model of the prefabricated dam is established in the existing pre-processing software Hypermesh, Marc Mentat, and Rhino, and material partitions are specified, including cast-in-place concrete, prefabricated concrete blocks, and mortar, to provide information for the subsequent identification of contact units. S2, further preprocessing work, using C# and FORTRAN programming languages ​​to write code 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, based on the material partition specified in S1, identifies the elements assigned to the mortar material as contact elements. This work is completed using code written in FORTRAN, automatically calculates the relevant information of the contact elements, specifies the properties of the contact elements in this step, and outputs the contact element information file for the performance analysis of prefabricated assembled dams. S4. The calculation program for the combined finite element method and the contact element method is written in FORTRAN language. The advantage of the contact element method is that it uses the traditional finite element integration rules to superimpose the properties of the contact elements into the overall stiffness matrix, ensuring that the overall stiffness matrix of the prefabricated dam is a symmetric positive definite matrix. The linear equation system is solved using Cholesky decomposition. S5 imports the model information file output from S2 and the contact element information file output from S3 into the calculation program developed in S4, and calculates the response of the prefabricated dam under different load combinations based on the input loads under different working conditions. S6 outputs the calculation results from S5. The output results are in binary format. The FORTRAN code is used to convert them into a specific format that can be recognized by the post-processing software Tecplot and GiD. The results are then input into the post-processing software to visualize the calculation results, quantitatively analyze the displacement and stress distribution of the prefabricated dam, and determine the performance of the prefabricated dam.

2. The static calculation method for prefabricated assembled dams according to claim 1, characterized in that: In S3, the contact element has 8 nodes, each node has 3 degrees of freedom, for a total of 24 degrees of freedom. x , y , z Using the global coordinate system, η, ξ, ζ Let be a local coordinate system. Let represent the displacement of each node of the contact element in the local coordinate system. Let $\mathbf$ be the displacement of each node in the element in the global coordinate system, and the relationship between the two is as follows: In the formula, The transformation matrix is ​​given; the average relative displacement between the upper and lower surfaces of the contact element can be expressed as: In the formula, It is a matrix of shape functions; It is the displacement vector of the unit's global coordinate system.

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

4. The static calculation method for prefabricated assembled dams according to claim 3, characterized in that: Elastic matrix of contact element The calculation formula is: In the formula, and It refers to the tangential stiffness of the contact element in two directions; It is the normal stiffness of the contact element.

5. The static calculation method for prefabricated assembled dams according to claim 4, characterized in that: In S3, the elastic matrix of the contact element is closely related to its contact state, namely closed, sliding, and open, and the calculation formula is as follows: In the formula, and It is the tangential stiffness of the contact element; It is the normal stiffness of the contact element; f and c These are the friction coefficient and cohesion of the contact unit; and Tangential stress components in two directions of the contact element; It is the normal stress component, that is, negative under compression and positive under tension; It is the initial gap between the contact element and the adjacent element surface.

6. The static calculation method for prefabricated assembled dams according to claim 5, characterized in that: In S3, the stresses in the normal and tangential directions of the contact element are calculated according to the following formula:

7. The static calculation method for prefabricated assembled dams according to claim 6, characterized in that: After obtaining the global stiffness matrix of the contact elements, the stiffness of the contact elements is integrated into the overall model stiffness matrix using the finite element stiffness integration rules to obtain the overall model stiffness matrix. The displacements of each node in the model are then calculated using the following formula: In the formula, The overall stiffness matrix of the model; This refers to the nodal displacement vectors in the model; This represents the nodal load vector.

8. The static calculation method for prefabricated assembled dams according to claim 7, characterized in that: In S3, during the static calculation of prefabricated dams, the contact state of contact elements in the prefabricated dam needs to be determined through iterative calculation. The iterative format for determining the contact state of contact elements is as follows: in: For the first i The overall stiffness matrix of step -1 changes with the contact state; In the formula, This is the set of seam units whose contact state changes between the two iterations; In the formula: For the first i The stress increment of the contact element under the assumption that the contact state does not change in the next iteration; For the first i The stress increment of the iteration, from the first iteration i- 1st iteration to the 1st i In the next iteration, if the contact state remains unchanged, then = ;otherwise:

9. The static calculation method for prefabricated assembled dams according to claim 8, characterized in that: in In each iteration, the contact state of the contact element is determined based on the average relative displacement of the calculated node, the incremental average relative displacement, and the stress components calculated under the assumed contact state. The stress increment of the contact element with the changed contact state is calculated according to Equation (14).

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