Premium
A new direct time integration method for the equations of motion in structural dynamics
Author(s) -
Katsikadelis J.T.
Publication year - 2014
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201200245
Subject(s) - independent equation , nonlinear system , equations of motion , mathematics , newmark beta method , ordinary differential equation , direct integration of a beam , differential equation , simple (philosophy) , representation (politics) , simultaneous equations , mathematical analysis , motion (physics) , numerical integration , term (time) , classical mechanics , physics , philosophy , epistemology , quantum mechanics , politics , political science , law , thermodynamics
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.