Improved High-order Hybrid Stress Elements Of Mindlin Plate Theory And Stability Analysis

The finite element method,as an important numerical method,has been highly valued by scholars and engineers due to its universality and effectiveness.With the development of finite element theory into a key component of computer-aided technology and structural simulation,it has been widely applied in practical engineering as a crucial tool for analyzing and simulating problems.Based on the finite element method,the stability of plate elements around high-order moderately thick plate hybrid stress elements is explored.Plate stability analysis is a fundamental and crucial research topic.When the load borne by the plate reaches the critical value,deformation or displacement jump phenomenon may occur in the structure.Mindlin plate theory has attracted much attention in the research field and has already derived many excellent plate elements.The use of finite element method for buckling analysis of Mindlin plate elements is currently one of the most effective numerical methods and plays an important role in engineering applications.This article mainly explores the following contents:Firstly,based on Mindlin plate theory,the hybrid stress element method is selected,and arbitrary-order Timoshenko beam functions are used for displacement interpolation.The classical Timoshenko beam function can solve the shear locking problem,but the elements constructed with it fail the non-zero constant shear force patch test.However,by using the high-order characteristics of the arbitrary order Timoshenko beam function,a third-order Timoshenko beam function is obtained and used to construct the boundary displacement interpolation function of the quadrilateral plate element,which can pass the strict convergence test of C0-1.The Airy stress function is selected for generalized force interpolation.Displacement and bending moment values are calculated through bending analysis to determine the optimal selection of 21 stress terms for stress interpolation,resulting in the construction of the QA8-R quadrilateral eight-node element described in the article.Secondly,the verification function of the enhanced patch testing is obtained based on the internal force equilibrium equation constructed by displacement,which is used for subsequent patch testing of the element.The geometric stiffness matrix in the stability analysis is improved through the refinement element method using the Serendipity interpolation function,and a refined geometric stiffness matrix with adjustable parameters is introduced to establish the finite element expression for buckling analysis.The number of stress interpolation parameters and the values of the adjustable parameters in the combined geometric stiffness matrix are determined through buckling stability analysis.Finally,the QA8-R element is applied to the buckling stability analysis of rectangular and sloping plates and compared with other types of elements under different boundary conditions,especially in the analysis of moderately thick plate under different boundary conditions.The numerical examples show that the element can pass the C0-1 patch test to ensure its strict convergence.In addition,the QA8-R element has higher computational accuracy for moderately thick plates under different boundary conditions and is more suitable for engineering applications.