The Modified Large Increment Method For Elastoplastic Analysis Of Plane Frame Strurtures

The most common finite element method in the current structural analysis is based on the matrix displacement method.Force method has some characteristics which are superior to the displacement method in structural design,structural optimization,stress concentration and material nonlinearity,but its research and development are far behind matrix displacement method,which is not suitable for computer processing is the most fundamental reason.Large Incremental Method(LIM)is a finite element method based on force method and generalized inverse matrix theory proposed in recent years,which completely overcomes the shortcomings that force method is not suitable for computerization.For the general statically indeterminate structure,there exists an arrayless solution to satisfy the equilibrium equation obtained by the node equilibrium relation,but only the solution satisfying the coordination equation is the correct solution.LIM uses the generalized inverse matrix principle to directly solve a special solution of the equilibrium equation,and changes the solution process to an optimization problem.In the nonlinear analysis of materials,compared with the displacement-based finite element method,LIM has the main advantages:(1)more accurate,the constitutive relations need not to be linearized,and it does not require a step-by-step approach,thus avoiding the development of cumulative errors,(2)more efficient,LIM was born with the capacity for parallel computation,without sub-structural division can be directly to solve the element constitutive equation in parallel.Because it separates the linear global equilibrium and compatibility equations from the possibly nonlinear local constitutive relations.The existing research on the large increment method is focused on the theoretical research and the expansion of the element library,however,the application of the nonlinear analysis of the complex skeletal structure is not enough.Therefore,the main work of this paper focuses on the application of LIM in the elastoplastic analysis of the plane frame.As follow is the main work of this paper.This paper discusses the application of LIM and contragadient law in complex planar skeletal structures,establishes the LIM basic governing equation of plane frame structure,and proposes the analysis approaches for complex boundary condition and composite joints.The illustrative example of linear elastic problem clearly reveals that its the accuracy and efficiency are the same as those of displacement-based finite element method.The elasto-plastic analysis of LIM in a planar frame is equivalent to an optimization problem with linear equality and nonlinear inequality constraints.The generalized gradient projection method is used to improve the iterative process of large increment method and the plastic hinge judgment is more accurate.It will not form misjudgment in the boundary of positive constraint set of inequality.When the new plastic hinge is added,there is no need to recalculate iterative initial value.The modified LIM greatly improves the calculation efficiency.Based on the Parallel Computing Toolbox(PCT)and Matlab Distributed Computing Server(MDCS)provided by Matlab,the parallel calculation in spatial domain is achieved.The maximum speedup ratio can reach 7.The comparison of the example shows 120% faster than ANSYS.The main innovation of this paper is that,proposing the analysis approaches for complex boundary condition and composite joints,improving large increment method for elastic perfectly plastic analysis of plane frame structures,making it more efficient and accurate,and realizing the parallelization of large increment method in spatial domain.