Fracture analysis and calculation method for complex high dam concrete structure based on near-field dynamics

Abstract

The application discloses a complex high dam concrete structure fracture analysis and calculation method based on near-field dynamics. The method firstly establishes a geometric model of the concrete structure, and constructs control equations of a macroscopic response region and a potential fracture region of the whole structure based on finite element theory (FEM) and near-field dynamics theory (PD); the finite element region and the near-field dynamics region are discretely interpolated by using an implicit format and a shape function, and a unified FEM-PD coupling system control equation is assembled by means of a coordination stiffness matrix and a coupling interface processing technology; the node and material point displacements are calculated by solving linear equations, and the material damage state is updated in real time according to a concrete damage constitutive relation and a critical fracture criterion; and the multiple crack propagation paths are automatically tracked based on the damage field evolution results. The application is suitable for fracture process analysis and safety evaluation of different types of complex high dam concrete structures.

Description

Technical Field

[0001] This invention relates to the field of fracture analysis of complex high dam concrete structures, and in particular to a calculation method for fracture analysis of complex high dam concrete structures based on near-field dynamics. Background Technology

[0002] In the field of civil engineering, fracture damage failure of critical concrete structures (such as long-span bridges, high-rise buildings, hydraulic structures, and nuclear power facilities) is one of the core issues affecting the safety and durability of engineering projects. As a typical quasi-brittle heterogeneous material, concrete, under complex static and dynamic loads, undergoes a progressive failure process from microscopic defects to macroscopic cracks, directly determining the structure's load-bearing capacity and service life. Therefore, developing a computational method capable of accurately predicting the entire process of crack initiation and propagation in concrete structures is of great significance for achieving performance-based design, life prediction, and safety control of engineering structures.

[0003] Currently, the finite element method (FEM), based on classical continuum mechanics, remains the most widely used numerical simulation tool for fracture analysis of concrete structures. While the FEM performs well in calculating continuous stress-strain fields, it has inherent theoretical limitations when simulating discontinuous problems such as fracture. The governing equations of the FEM require spatial differentiability of the displacement field, making it difficult to naturally describe crack initiation and arbitrary path propagation. During simulation, crack locations are typically preset or complex fracture criteria are relied upon, and cumbersome mesh re-division techniques are required to track crack evolution. This process is not only computationally inefficient but also highly dependent on user experience, making it difficult to effectively simulate complex failure behaviors common in concrete, such as multi-crack initiation, interaction, convergence, and branching. These technical bottlenecks severely restrict the high-reliability design and safety assessment of concrete structures. Therefore, there is an urgent need in this field for a novel numerical method capable of adaptively simulating the entire process of concrete material damage to fracture. The emerging peri-field dynamics theory, by introducing integral forms of motion equations to replace traditional differential equations, fundamentally avoids the singularity of crack tip solutions, providing a new path to overcome these technical challenges. Based on this theory, this invention proposes a high-precision and high-efficiency fracture analysis and calculation method applicable to complex high dam concrete structures, aiming to provide an advanced and reliable calculation tool for fracture safety assessment in civil engineering. Summary of the Invention

[0004] The main objective of this invention is to provide a fracture analysis and calculation method for complex high dam concrete structures based on peri-field dynamics. Addressing the shortcomings of existing pure peri-field dynamics methods, which suffer from high computational costs across the entire area, and the finite element method's inability to naturally simulate crack propagation, this invention provides a fracture analysis method that adaptively couples finite element method and peri-field dynamics. This method can significantly improve the computational efficiency of overall fracture analysis of complex high dam concrete structures while maintaining the accuracy of fracture simulation in key areas.

[0005] To achieve the above objectives, this invention provides a fracture analysis and calculation method for complex high dam concrete structures based on near-field dynamics. The method includes the following steps:

[0006] S1. Establish a two-dimensional geometric model of the complex high dam concrete structure in ABAQUS software, and perform scaled boundary finite element mesh generation to generate an initial mesh model. Simultaneously, preset the material parameters, near-field range, and critical displacement criteria for near-field dynamics to prepare data for subsequent adaptive transformation.

[0007] S2. Apply loads and constraints to the initial mesh model established in step S1, and perform implicit static solutions to obtain the displacements of the complex high dam concrete structure. Compare the solved displacements with the preset critical displacement criteria, select regions whose displacements exceed the critical displacement criteria, define them as high displacement regions, and then define these high displacement regions as fracture regions.

[0008] S3. Convert the scaled boundary finite element mesh of the fracture region marked in step S2 into near-field dynamic material points. Establish the element stiffness matrix of the scaled boundary finite element mesh in the non-fracture region, establish the bond stiffness matrix of the near-field dynamic material points in the fracture region, and assemble the stiffness matrices of the two regions to ensure the transfer of displacement between the scaled boundary finite element mesh and the near-field dynamic material points, thereby constructing a unified SBFEM-PD global linear equation system.

[0009] S4. Perform load step solution of the SBFEM-PD global linear equation system. The load in S2 is applied in multiple load steps. In each load step calculation, the global linear equation system is solved, and the displacements of the fracture region and the non-fracture region are updated simultaneously. In the fracture region, based on the updated material point displacements and the critical displacement criterion defined in step S1, the near-field dynamic material points that have reached the critical displacement are determined, and the damage degree and bond stiffness matrix of the fracture region are updated in real time. The damage degree of the fracture region is checked. If the damage degree increases, the updated bond stiffness matrix is ​​used to continue solving in the current load step until the solution converges and enters the next load step.

[0010] S5. After entering the next load step, first determine whether the fracture region needs to be expanded based on the updated displacements of the fractured and non-fractured regions. If the displacement of the non-fractured region exceeds the critical displacement criterion, it will be converted into a fractured region, and the process will return to step S4 to continue solving. Repeat steps S4 to S5 until all load steps are calculated.

[0011] The beneficial effects of this invention are:

[0012] (1) The present invention adopts the adaptive coupling method of proportional boundary finite element and near-field dynamics to simulate the displacement and damage of the fracture area and non-fracture area of ​​complex high dam concrete structure in a regional manner, thereby realizing the unified calculation of deformation and crack initiation and propagation, and realizing high-fidelity simulation and visualization of the entire fracture process of complex high dam concrete structure.

[0013] (2) Based on a unified implicit solution framework, this invention transforms the complex fracture problem into an iterative solution of the coupled SBFEM-PD global linear equation system. While avoiding the time step limitation of traditional explicit methods, it ensures the stability and convergence of numerical calculations, and finally can efficiently and accurately obtain the crack propagation path of complex high dam concrete structures under load.

[0014] (3) Through the dynamic identification of critical displacement criteria and automatic model conversion mechanism, this invention can accurately analyze the fracture behavior of complex high dam concrete structures under different geometric shapes, load conditions and material models. Its high degree of automation and robustness verify that this method has wide and flexible applicability in engineering practice. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the fracture analysis and calculation method for complex high dam concrete structures according to the present invention.

[0016] Figure 2 A schematic diagram of the geometric model of a complex high dam concrete structure;

[0017] Figure 3 A schematic diagram of the mesh discretization of a complex high dam concrete structure;

[0018] Figure 4 The figures show a comparison of the cracking results of complex high dam concrete structures calculated by the present invention and other methods, where (a) is the proportional boundary finite element-peripheral dynamics, (b) is the finite element-peripheral dynamics, and (c) is the peripheral dynamics. Detailed Implementation

[0019] It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. The realization of the invention's objectives, functional characteristics, and advantages will be further explained in conjunction with the embodiments and with reference to the accompanying drawings.

[0020] like Figure 1 As shown, Figure 1 This is a flowchart illustrating the fracture analysis and calculation method for complex high dam concrete structures described in this invention. The detailed method includes the following steps:

[0021] S1. Establish a two-dimensional geometric model of the complex high dam concrete structure in ABAQUS software, and perform scaled boundary finite element mesh generation to generate an initial mesh model. Simultaneously, preset the material parameters, near-field range, and critical displacement criteria for near-field dynamics to prepare data for subsequent adaptive transformation.

[0022] S2. Apply loads and constraints to the initial mesh model established in step S1, and perform implicit static solutions to obtain the displacements of the complex high dam concrete structure. Compare the solved displacements with the preset critical displacement criteria, select regions whose displacements exceed the critical displacement criteria, define them as high displacement regions, and then define these high displacement regions as fracture regions.

[0023] S3. Convert the scaled boundary finite element mesh of the fracture region marked in step S2 into near-field dynamic material points. Establish the element stiffness matrix of the scaled boundary finite element mesh in the non-fracture region, establish the bond stiffness matrix of the near-field dynamic material points in the fracture region, and assemble the stiffness matrices of the two regions to ensure the transfer of displacement between the scaled boundary finite element mesh and the near-field dynamic material points, thereby constructing a unified SBFEM-PD global linear equation system.

[0024] S4. Perform load step solution of the SBFEM-PD global linear equation system. The load in S2 is applied in multiple load steps. In each load step calculation, the global linear equation system is solved, and the displacements of the fracture region and the non-fracture region are updated simultaneously. In the fracture region, based on the updated material point displacements and the critical displacement criterion defined in step S1, the near-field dynamic material points that have reached the critical displacement are determined, and the damage degree and bond stiffness matrix of the fracture region are updated in real time. The damage degree of the fracture region is checked. If the damage degree increases, the updated bond stiffness matrix is ​​used to continue solving in the current load step until the solution converges and enters the next load step.

[0025] S5. After entering the next load step, first determine whether the fracture region needs to be expanded based on the updated displacements of the fractured and non-fractured regions. If the displacement of the non-fractured region exceeds the critical displacement criterion, it will be converted into a fractured region, and the process will return to step S4 to continue solving. Repeat steps S4 to S5 until all load steps are calculated.

[0026] Further, in step S1, the material parameter expression for the pre-defined near-field dynamics is:

[0027]

[0028]

[0029]

[0030]

[0031] in, Represents the microscopic modulus function. Represents the initial micromodulus. Represents the kernel function. Indicates the historical dependency function, Indicates the radius of the family. Indicates the relative positions of two substance points. Indicates the elastic modulus. s π represents elongation, and π represents pi. The critical elongation is expressed as:

[0032]

[0033] in, G 0 represents the fracture energy.

[0034] Introducing a quantitative equation into the material parameters The degree of damage in a material point is characterized by the following expression:

[0035]

[0036] in, and Representing two material points, Representing a point of matter The tribe, Representing a point of matter The volume.

[0037] Furthermore, in step S3, in near-field dynamics, the interaction between matter points is conceptualized as a rod element in the finite element method. Therefore, for a two-dimensional problem, in the local coordinate system, the interaction between two matter points x... i and x j The bond stiffness matrix is ​​specifically expressed as:

[0038]

[0039] in, Represents the material point x i volume, Represents the material point x j volume, It represents the distance between two material points.

[0040] Two material points x in the global coordinate system i and x j The bond stiffness matrix is ​​specifically expressed as:

[0041]

[0042] coordinate transformation matrix T for:

[0043]

[0044] in, l and m Indicates the coordinate transformation factor;

[0045] Finally, the two material points x in the global coordinate system i and x j The bond stiffness matrix is ​​expressed as:

[0046]

[0047] For a scaled boundary finite element mesh, any point in the Cartesian coordinate system In the proportional boundary coordinate system, it is represented as:

[0048]

[0049]

[0050] in, Represents radial coordinates, Indicates circumferential coordinates, and Represented as nodal coordinates in Cartesian coordinate system. The function represents a shape, and its specific expression is:

[0051]

[0052] The transformation relationship between the Cartesian coordinate system and the proportional boundary coordinate system is expressed as follows:

[0053]

[0054] in, , , and They represent respectively to , , and The partial derivative, The Jacobian matrix is ​​expressed as:

[0055]

[0056] in, and Indicates to and Find the partial derivative, i.e. and .

[0057] Based on the fundamental equations of static equilibrium, the governing equations of the scaled boundary finite element mesh are derived as follows:

[0058]

[0059] in, Indicates displacement. Indicates displacement pair The first-order partial derivative, Displacement pair The second-order partial derivative, , and It is a coefficient matrix, and its specific expression is:

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067] in, Represents the elasticity matrix. and Represents the strain matrix. and Represents the coefficient matrix. Representing shape function pairs The first-order partial derivative, This represents the determinant of the Jacobian matrix.

[0068] To solve the governing equations of the scaled boundary finite element mesh, the Hamiltonian matrix is ​​introduced:

[0069]

[0070] Among them, the superscript " " indicates the transpose of a matrix, with the superscript " " denotes the inverse of the matrix.

[0071] Finally, the element stiffness matrix of the scaled boundary finite element mesh is obtained:

[0072]

[0073] in, and This represents the eigenvector.

[0074] The assembly expression for the element stiffness matrix and the bond stiffness matrix of the near-field dynamic material points in the scaled boundary finite element mesh is as follows:

[0075]

[0076] Finally, the global linear equation system of SBFEM-PD is obtained:

[0077]

[0078] in, This represents the sum of displacements in the fractured and non-fractured regions. Indicates load.

[0079] In this embodiment, a geometric model of a complex high dam concrete structure is established. Based on the scaled boundary finite element theory and peri-field dynamics theory, the basic governing equations for the non-cracked and cracked regions are constructed respectively. An implicit scheme is used to discretize the scaled boundary finite element and peri-field dynamics, and the overall stiffness matrix is ​​assembled to derive a unified SBFEM-PD global linear equation set. This linear equation set is solved, and the damage degree is updated in real time according to the critical displacement criterion during the calculation process, further revealing the crack evolution process of the complex high dam concrete structure. This invention effectively balances computational accuracy and efficiency in fracture analysis, significantly reducing the computational resources required for full-life-cycle fracture simulation of complex high dam components.

[0080] Furthermore, to verify the applicability, accuracy, and robustness of this invention in fracture analysis of complex high dam concrete structures, the computational performance of this method will be examined by comparing different methods, and crack initiation and propagation analysis of complex high dam concrete structures under static tensile loads will be carried out.

[0081] like Figure 2 As shown, a notched concrete structure with an eccentric circular hole is given. The geometric parameters of the structure are width. ,high eccentric circular hole diameter Length of the gap Distance from bottom The material parameter is the elastic modulus. Poisson's ratio The structure was initially discretized into 3710 scaled boundary finite element sections, such as... Figure 3 As shown. In the near-field dynamics model, the material point spacing is set to Δ = 0.09 cm, and the near-field radius is... δ =3.15Δ, critical bond elongation s0 = 0.015. Loading is achieved by gradually applying a preset displacement of 0.3 cm over 150 load steps.

[0082] The crack propagation results simulated by this method are basically consistent with those of other methods, such as... Figure 4 As shown. Furthermore, the computation time for scaled boundary finite element-peripheral dynamics (this method) is only 3.6 minutes, the computation time for finite element-peripheral dynamics reaches 43 minutes, and the computation time for peripheral dynamics reaches 160 minutes, which fully demonstrates the computational speed advantage of this method.

Claims

1. A method for fracture analysis and calculation of complex high dam concrete structure based on near-field dynamics, characterized in that, The method comprises the following steps: S1, a two-dimensional geometric model of a complex high dam concrete structure is established in ABAQUS software, and a proportional boundary finite element mesh is divided, and an initial mesh model is generated; at the same time, material parameters, a near-field range and a critical displacement criterion of near-field dynamics are preset, and data preparation is made for subsequent adaptive conversion; S2, a load and a constraint are applied to the initial mesh model established in step S1, and an implicit static force solution is performed to obtain the displacement of the complex high dam concrete structure; the displacement obtained by the solution is compared with the preset critical displacement criterion, and the area whose displacement exceeds the critical displacement criterion is selected as a high displacement area, and then the high displacement area is defined as a fracture area; S3, the proportional boundary finite element mesh of the fracture area marked in step S2 is converted into a near-field dynamic particle; an element stiffness matrix of the proportional boundary finite element mesh is established in a non-fracture area, a bond stiffness matrix of the near-field dynamic particle is established in a fracture area, and the stiffness matrices of the two areas are assembled to ensure the transmission of displacement between the proportional boundary finite element mesh and the near-field dynamic particle, so as to construct a unified SBFEM-PD overall linear equation set; S4, a load step solution of the SBFEM-PD overall linear equation set is performed; the load in S2 is applied by multiple load steps, and in each load step calculation, the overall linear equation set is solved, and the displacement of the fracture area and the non-fracture area is updated; in the fracture area, the near-field dynamic particle whose fracture reaches the critical displacement is judged based on the updated particle displacement and the critical displacement criterion defined in step S1, and the damage degree and the bond stiffness matrix of the fracture area are updated in real time; the damage degree of the fracture area is checked, and if the damage degree increases, the updated bond stiffness matrix is used to continue solving at the current load step until the solution converges to the next load step; S5, after entering the next load step, first, whether the fracture area needs to be expanded is judged according to the updated displacement of the fracture area and the non-fracture area; if the displacement of the non-fracture area exceeds the critical displacement criterion, the fracture area is converted, and the step S4 is returned to continue solving; steps S4 to S5 are executed in a loop until the calculation of all load steps is completed.

2. The method for fracture analysis of complex high dam concrete structure based on near-field dynamics according to claim 1, wherein, In the step S1, the expression of the material parameters of the near-field dynamics is preset as: wherein, denotes a micro-modulus function, denotes an initial micro-modulus, denotes a kernel function, denotes a history-dependent function, denotes a radius of the family, denotes a relative position of two material points, denotes an elastic modulus, s denotes an elongation, π denotes a circular constant, denotes a critical elongation, denoted as: wherein G 0 is the energy of rupture; A quantitative equation is introduced into the material parameters to characterize the damage degree in the material points, which is expressed as wherein, and denotes two material points, denotes a material point of the family, denotes the volume of a material point .

3. The method for fracture analysis of complex high dam concrete structure based on near-field dynamics according to claim 2, characterized in that, In the step S3, in near-field dynamics, the interaction between material points is conceptualized as a bar element in the finite element method; thus, for a two-dimensional problem, the bond stiffness matrix of two material points x i and x j is specifically expressed as: wherein denotes the volume of the material point x i , denotes the volume of the material point x j , denotes the distance between the two material points; The bond stiffness matrix of two material points x i and x j under the global coordinate system is specifically expressed as: Coordinate conversion matrix T is: wherein l and m denotes a coordinate conversion factor; Finally, the bond stiffness matrix of two material points x i and x j in the global coordinate system is expressed as: For the scaled boundary finite element mesh, the scaled boundary finite element mesh is a special case of the boundary element method In the scaled boundary coordinate system, it is expressed as wherein, denotes the radial coordinate, denotes the circumferential coordinate, and denotes the nodal coordinates in Cartesian coordinate system, denotes the shape function, the specific expression is: The transformation relationship between the Cartesian coordinate system and the proportional boundary coordinate system is represented as: where , , and denote the partial derivatives of , , and , denotes the Jacobian matrix, expressed as: wherein and denotes the partial derivative with respect to and i.e. and ; Based on the static equilibrium basic equation, the control equation of the proportional boundary finite element mesh is derived: wherein denotes the displacement, denotes the first-order partial derivative of the displacement with respect to denotes the second-order partial derivative of the displacement with respect to , and is a coefficient matrix, the specific expression of which is: wherein denotes the elastic matrix, and denotes the strain matrix, and denotes the coefficient matrix, denotes the first partial derivative of the shape function pair with respect to denotes the determinant of the Jacobian matrix; In order to solve the control equation of the proportional boundary finite element mesh, the Hamilton matrix is introduced: where the superscript T denotes the transpose of a matrix, and the superscript -1 denotes the inverse of a matrix. Finally, the element stiffness matrix of the proportional boundary finite element mesh is obtained: wherein and denotes a feature vector; The assembly expression of the element stiffness matrix of the proportional boundary finite element mesh and the bond stiffness matrix of the near-field dynamic particle is: Finally, the SBFEM-PD overall linear equation set is obtained: wherein, represents the sum of the displacements of the fractured and non-fractured regions, represents the load.

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