Abstract
A new incremental technique is presented which facilitates the numerical solution of static and dynamic finite deflection problems. By means of this technique, termed the Rate Equation Method, a set of linear differential equations in the displacement rates and stress rates are obtained from the nonlinear differential equations associated with finite deflections. These linear differential equations are solved numerically for the rate variables which in turn are integrated forward in time to yield the displacements and stresses at each time increment. By using second order finite differences to express the rates of accelerations in terms of velocities, static and dynamic problems may be solved by the identical procedure. To illustrate the details of the method, static and dynamic geometrically nonlinear deformations of cables under various loads are investigated and numerical results presented for several cases.
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