Research On High-precision Stress Field Construction Method Based On Scaled Boundary Finite Element

Stress is the basic basis for structural strength checking.For complex structures,the finite element method is often used to calculate the stress response of the structure,but the calculation results are related to the finite element mesh size and arrangement.It is necessary to use element mesh densification,increase the interpolation order,and stress recovery to get the reasonable stress calculation results.Methods such as post-processing to obtain a more reasonable stress field are difficult to achieve in actual engineering,especially for the locations of sudden geometrical changes such as cracks and concave corners,where dense meshes are required to better characterize in these locations to present the singular stress field.The solution of the Scaled Boundary Finite Element Method(SBFEM)has semi-analytical characteristics.Compared with finite element,it is very suitable for solving problems such as singular stress field and infinite domain.Based on the SBFEM,this paper has conducted the research on the calculation method to improve the stress accuracy.The main research contents include:1.For the standard SBFEM with a point as the similar center,(1)the influence of the element shape function and the similar center point arrangement method on the accuracy of the calculation result is studied.The results show that higher-order elements are easier to obtain convergent and reliable solutions;(2)The element stress smoothing method is used to obtain the improved nodal stress of the proportional boundary finite element surface discrete element.The calculation results of the crack tip stress field show that it is consistent with the finite element Compared with the method(FEM),the proportional boundary finite element method can describe the singular stress field at the crack tip with fewer nodes.2.Based on the posterior error calculation method proposed by Zienkiewicz-Zhu(ZZ),the stress error index calculation formula of the three-dimensional proportional boundary finite element element is deduced.It can be found through calculation examples that the stress error index gradually decreases as the mesh is refined,which preliminarily verifies that the stress error index can be used as a basis for judging the calculation accuracy of the current solution to the stress field.3.It is proposed that the line as the similar center can be used to describe the singular stress field of the entire crack front or the intersection of the concave angle.First,based on the Hamilton variational principle,the finite-field SBFEM control differential equation with the line as the similarity center is derived.Then,the Runge-Kutta method is used to solve the equation to obtain the element boundary stiffness,and then the displacement of the element surface node can be solved.Obtain the strain and stress field inside the element.For the examples of cantilever straight beams and unilateral cracks,the calculation results of the displacement field and the stress field are in good agreement with the finite element results,which verifies the accuracy of the method in this paper.