Numerical integration of nonlinear structural models

The analysis of the response of a structural dynamic system involves modeling the system in discretized form as a set of linear or nonlinear second order differential equations: [M]{U} + [C]{U} + [K]{U} +{N(U)} = {F(t)} In the above differential equation, {U} is a large n-dimensional displacement vector, [M], [C], and [K] are symmetric nxn mass, damping and stiffness matrices and {N}, {F} are the nonlinear force vector and external excitation, respectively. For the nonlinear case, it is necessary to obtain solutions via numerical integration of the equations of motion. As part of my thesis work, a new approach to numerical integration of the nonlinear equations of motion is proposed. The method is an efficient technique to obtain the response of any dynamic system, as it works in close approximation with Runge-Kutta fourth-order method, on linear as well as nonlinear models. The basic idea behind the method is to define two gauss points in each integration time step (between tn-i & tn) and to evaluate the response at the gauss points using a standard explicit method. The average values at these gauss points are used to calculate displacement, velocity and acceleration at time step tn+1-