| Design and analysis of engineering structures is an indispensable process of its con-struction,and the response analysis of structure under dynamic load is an essential part of structural analysis.Due to the complex form of the real structure,it is difficult to find the analytical dynamic response in dynamic analysis.So numerical methods are com-monly used to solve the structural dynamic response,and the numerical algorithms of initial value problems have become the focus of research on structural dynamics.The weak form quadrature element method（QEM）,proposed by Zhong et al.,has achieved great success in analysis of various problems since the early of the 21th century.The weak form QEM can be applied to various0and1-continuity problems with high ac-curacy and efficiency.However,the weak form QEM has not been applied to structural dynamic analysis.Therefore,the solution of structural motion equations on the basis of the weak form QEM is the main point of this thesis.The highlights of the present work are summarized as follows:（1）A new functional of linear elastic structural motion equation is proposed with the introduction of time-reversed function to overcome the drawback of Hamilton princi-ple.On the basis of the new functional,a weak form quadrature element algorithm with conditional stability is developed.Compared with some time integration methods,this al-gorithm achieves higher accuracy and computational efficiency by dividing the concerned time domain into several time elements.（2）Based on a weighted-residual weak form,a weak form quadrature element algo-rithm for linear elastic problems is developed.Gauss-Radau integration and generalized differential quadrature analog are used to avoid the singularity of this weak form.The present algorithm is conditionally stable and owns numerical dissipation.（3）The weak form quadrature element method is applied on two classes of nonlinear equation–Duffing equation and Mathieu’s equation.An adaptive parameter-adjusting technique is proposed to select the number of elements and the number of integration points in one element adaptively.This algorithm performs better than other time inte-gration methods on several numerical examples with higher accuracy and much lower computational cost.（4）The second-order structural motion equation is converted into first-order equa-tion and a new weak form quadrature element algorithm with better numerical properties is proposed based on the first-order equation.This algorithm achieves unconditional sta-bility and shows great numerical dissipation.It is shown that the algorithm can be used to solve wave propagation problems,nonlinear problems and elastic-plastic time history analysis of structure.Compuational efficiency of the algorithm can be enhanced by apply-ing the weak form quadrature element method spatially to reduce the number of degrees of freedom. |
