华中科技大学学报（自然科学版）2025，Vol.53Issue(6)：95-101,7.DOI:10.13245/j.hust.250613
三维几何非线性问题的格点型有限体积法研究
Research on cell-vertex finite volume method for three-dimensional geometric nonlinear problems
摘要
Abstract
A cell-vertex finite volume method for elastic structures was developed to study three-dimensional geometric nonlinear problems.The method was based on the cell-vertex finite volume method to solve the governing equation described by Kirchhoff stress.The computational domain could be divided by unstructured grids such as tetrahedron and hexahedron,which had strong applicability to irregular shape problems.The initial configuration was used as the reference configuration for calculation,and the governing equations were discretized based on the cell-vertex finite volume method.The linear elastic results were used as the initial values,nonlinear equations were iteratively solved by the Newton-Raphson method,and then the solving program was developed based on the C++programming language.The program was used to analyze the large deformation problems of cantilever beam,clamping beam and shell under different loads.Numerical calculation results show that the error between the cell-vertex finite volume method solution and the analytical solution does not exceed 3%,which verifies the correctness of the solution program.Compared with the initial field of 0,the calculation efficiency can be significantly improved by using the linear elastic calculation results as the iterative initial field.Tetrahedral,hexahedral and other grids can effectively deal with irregular structural problems,and the calculation results are in good agreement with those obtained by other methods.关键词
三维几何非线性问题/格点型有限体积法/有限变形/全拉格朗日格式/迭代求解Key words
three-dimensional geometric nonlinear problems/cell-vertex finite volume method/finite deformation/total Lagrange formulation/iterative solution分类
数理科学引用本文复制引用
龚京风,李晨琦,宣领宽,严楚..三维几何非线性问题的格点型有限体积法研究[J].华中科技大学学报（自然科学版）,2025,53(6):95-101,7.基金项目
汉江国家实验室开放基金资助项目(KF2024016) （KF2024016）
国家自然科学基金青年基金资助项目(51909197). （51909197）
