Global Formulation of Conservative Time Integration by the Increment of the Geometric Stiffness

Abstract

A momentum and energy conserving time integration algorithm is developed for the motion of elastic bodies described in terms of the quadratic Green strain. Momentum conserving algorithms are formulated from an integral of the equations of motion, and energy conservation has traditionally been obtained by evaluating the internal forces by combining the mean value of stresses and virtual strains at the element level [1]. It is here demonstrated that momentum and energy conservation can be obtained from the classic central difference formulation by including an extra global term in the form of the increment of the geometric stiffness matrix. The geometric stiffness matrix is usually available in assembled form in existing programs, and thus a global form is attained that avoids the need for modifying the classic element implementation.