Research On Structural Nonlinear Algorithm Based On Orthogonal Constraints

With the development of constructional material and methods,most structures show obvious geometric nonlinearity.Geometric nonlinearity has become the focus of engineering structures and it is increasingly important to reasonably analyze the buckling and post-buckling properties of structures.Incremental iterative finite element analysis method is one of the most commonly used methods to solve the structural nonlinear response.Different incremental iteration methods have different precision and efficiency.Based on the updated Lagrangian formulation,the theoretical basis of incremental iteration methods is described in detail in this study.Based on the orthogonal constraints,the generalized displacement control(GDC)method uses the generalized stiffness parameter(GSP)to detect the stiffness change of the structure and adjust the incremental step size and loading direction.When solving nonlinear structures,GDC has shown high accuracy.Based on the generalized displacement control method,this study presents a new attempt to analyze the post-buckling of structures by using only the elastic stiffness matrix.Based on the rigid-body rule,nodal forces of elements can be calculated with only elastic stiffness matrix involved.In the predictor,the stiffness matrix only affects the accuracy and efficiency,so it is required to accurately reflect the direction of iteration.Theoretically,the nonlinear problem can be solved using only the elastic stiffness.Some typical examples with large displacements and large deformations are selected to verify the accuracy of solving the structure using only the elastic stiffness matrix.The results show that even the sensitive structures also can be gained better computational accuracy and efficiency by using only elastic stiffness matrix.The elastic stiffness matrix is simple and clear,and the method does not solve other high-order and complex stiffness matrices,Therefore,the new attempt is simple and effective.The convergence criterion of orthogonal iteration is an effective method to eliminate errors.In this study,the iteration mechanism of orthogonal constraints is described in detail,and a variety of iterative algorithms are extended based on the orthogonal constraints.The first iteration determines the incremental step size and the loading direction,and the loading direction is determined by the stiffness matric.The subsequent iterations are to eliminate the error caused by linear calculation in the first iteration,and the iteration direction will be orthogonal to the reference direction vector.The incremental iteration method obtained by different orthogonal constraints will also have different calculation efficiency.Under the same condition,it will be more efficient to update the load increment factor expression in time with the iteration.