CN-122021137-A - Lagrange large deformation finite element analysis interpolation method for geotechnical engineering

CN122021137ACN 122021137 ACN122021137 ACN 122021137ACN-122021137-A

Abstract

The invention relates to a Lagrange large deformation finite element analysis interpolation method for geotechnical engineering, which adopts a super convergence recovery technology and a unique unit method to map state variables in old grids into new grids, and adopts a method of combining nearest neighbor with unit shape function extrapolation aiming at the interpolation error problem caused by boundary effect, thereby effectively improving the mapping precision of model state variables, improving the convergence of large deformation finite element calculation and providing stable and reliable technical support for geotechnical engineering large deformation finite element analysis.

Inventors

XIE RENJUN
JIAO JINGANG
Di Tongyu
ZHANG YOUHU
XU GUOXIAN
ZOU XIN
ZHANG XUFENG

Assignees

中海石油(中国)有限公司
中海石油（中国）有限公司北京研究中心

Dates

Publication Date: 20260512
Application Date: 20260115

Claims (7)

1. The Lagrange large deformation finite element analysis interpolation method for geotechnical engineering is characterized by comprising the following steps of: Step (1), according to the calculation results of a plurality of small-strain finite element analysis models which are analyzed and decomposed by the large-deformation finite element of geotechnical engineering, reading state variable information of each small-strain finite element analysis model to form a reference field; Step (2), identifying a reference field boundary and establishing a super-convergence restoration patch; step (3), recovering the integral point information of the reference field to the node based on the super-convergence recovery patch; Step (4), traversing the super-convergence patch to obtain recovery information of all nodes except boundary nodes of the reference field; step (5), obtaining the recovery information of the boundary nodes of the reference field by adopting a mode of combining nearest neighbor and unit shape functions, thereby finishing the information recovery of the nodes in the reference field; Step (6), based on the reference field which completes the recovery of all node information, a new grid is established, and the integral point coordinates of the new grid are calculated by adopting a shape function to form a target field; step (7), determining the mapping relation between the integration point or node of the target field and the unit of the reference field based on a unique unit method; Step (8), adopting a shape function interpolation or nearest neighbor method, and assigning values to the target field according to the information of the reference field; Step (9), recalculating a corresponding small-strain finite element analysis model according to the assigned target field; And (10) repeating the previous steps until the calculation of the large deformation analysis is completed.
2. The method of claim 1, wherein in step (1) the state variable information comprises grid integral point stress, material parameters, node pore pressure.
3. The method of claim 1, wherein in step (2), the super-healing recovery patch is composed of a plurality of units, and a node common to the units is a patch anchor.
4. A method according to claim 3, wherein in the step (3), the integral point information in the patch is fitted by using a quadratic polynomial and a least square method, and finally the node information in the center of the patch is recovered by using the quadratic polynomial obtained by fitting, including the anchor point and the midpoint of the edge adjacent to the anchor point, and the polynomial fitting effect in the patch is evaluated by using a decision coefficient R 2 , and when the preset effect is not achieved, the node information in the center of the patch is recovered by using a unit-shaped function extrapolation method.
5. The method according to claim 1, wherein in the step (7), a rectangular box and shape function calculation is used to determine a mapping relationship between an integration point or node of the target field and a unit of the reference field.
6. The method of claim 5, wherein in the step (8), the object field information is obtained by interpolation of a shape function for the object field integration points and nodes hitting the reference field unit, and the object field information is obtained by nearest neighbor method for the object field integration points and nodes not hitting the reference field unit.
7. A computer storage medium, characterized in that a computer program is stored, which computer program, when being executed by a processor, implements the method of any of claims 1 to 6.

Description

Lagrange large deformation finite element analysis interpolation method for geotechnical engineering Technical Field The invention relates to the technical field of geotechnical engineering numerical simulation, in particular to a Lagrange large deformation finite element analysis interpolation method for geotechnical engineering. Background In geotechnical engineering numerical simulation of an oil-gas jack-up platform, large deformation finite element analysis is a key means for researching deformation mechanism, stress evolution rule and damage mode of a geotechnical material under nonlinear conditions. However, the conventional Lagrangian finite element method is prone to computational interruption due to grid distortion when dealing with large deformation problems. In order to realize more accurate finite element simulation on the problem of large deformation of the rock and soil, the prior art often needs to introduce a complex rock and soil constitutive model capable of truly reflecting the mechanical response of the soil body. The model is different from the traditional total stress model, not only can simulate the generation and dissipation of the pore water pressure in the soil body in the large deformation process, but also can reflect the softening and hardening behaviors of the soil body strength. However, the complex geotechnical constitutive model generally has the problems of poor convergence, low calculation efficiency and the like, and is particularly difficult to apply under the condition of large deformation. Based on the method, a small-strain heavy grid interpolation technology (RITSS, REMESHING AND Interpolation Technique WITH SMALL STRAIN) is used for decomposing a large deformation problem into a plurality of continuous small deformation problems according to the difference of strain magnitudes, and the advantages of good convergence and wide applicability of Lagrange small deformation analysis are utilized, so that the effective application of the complex constitutive model in large deformation finite element simulation is realized. However, how to realize accurate transfer of state variables between the small deformation finite element analysis steps is an important technical difficulty affecting the feasibility of large deformation analysis. Because the rock-soil constitutive model has the characteristics of strong nonlinearity and difficult convergence, numerical errors are easily introduced in the variable transmission process, so that subsequent calculation is difficult to converge, and the numerical stability of large-deformation finite element analysis is seriously affected. Disclosure of Invention Aiming at the problems, the invention aims to provide the Lagrange large deformation finite element analysis interpolation method for geotechnical engineering, which combines a super convergence recovery technology and a unique unit interpolation algorithm, effectively improves the mapping precision of model state variables, improves the convergence of large deformation finite element calculation and provides stable and reliable technical support for geotechnical engineering large deformation finite element analysis. In order to achieve the above purpose, the present invention adopts the following technical scheme: In a first aspect, the present application provides a lagrangian large deformation finite element analysis interpolation method for geotechnical engineering, including: Step (1), according to the calculation results of a plurality of small-strain finite element analysis models which are analyzed and decomposed by the large-deformation finite element of geotechnical engineering, reading state variable information of each small-strain finite element analysis model to form a reference field; Step (2), identifying a reference field boundary and establishing a super-convergence restoration patch; step (3), recovering the integral point information of the reference field to the node based on the super-convergence recovery patch; Step (4), traversing the super-convergence patch to obtain recovery information of all nodes except boundary nodes of the reference field; step (5), obtaining the recovery information of the boundary nodes of the reference field by adopting a mode of combining nearest neighbor and unit shape functions, thereby finishing the information recovery of the nodes in the reference field; Step (6), based on the reference field which completes the recovery of all node information, a new grid is established, and the integral point coordinates of the new grid are calculated by adopting a shape function to form a target field; step (7), determining the mapping relation between the integration point or node of the target field and the unit of the reference field based on a unique unit method; Step (8), adopting a shape function interpolation or nearest neighbor method, and assigning values to the target field according to the information of the reference field; St