A new direct time integration method for the equations of motion in structural dynamics

作者：Katsikadelis John T^*

来源：ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 2014, 94(9): 757-774.

DOI：10.1002/zamm.201200245

• Equations of motion
• structural dynamics
• integral equations
• analog equation method
• differential equations
• numerical solution

A direct time integration method is presented for the solution of the equations of motion describing the dynamic response of structural linear and nonlinear multi-degree-of-freedom systems. It applies also to large systems of second order differential equations with fully populated, non symmetric coefficient matrices as well as to equations with variable coefficients. The proposed method is based on the concept of the analog equation, which converts the coupled N equations into a set of single term uncoupled second order ordinary quasi-static differential equations under appropriate fictitious loads, unknown in the first instance. The fictitious loads are established from the integral representation of the solution of the substitute single term equations. The method is simple to implement. It is self starting, unconditionally stable and accurate and conserves energy. It performs well when large deformations and long time durations are considered and it can be used as a practical method for integration of the equations of motion in cases where widely used time integration procedures, e. g. Newmark's, become unstable. Several examples are presented, which demonstrate the efficiency of the method. The method can be straightforward extended to evolution equations of order higher than two.

• 出版日期2014-9