This paper completes a preceeding paper on the algebraic formulation of elastostatics [Tonti, Zarantonello (2009)]. It shows how to obtain a numerical formulation for elastodynamics by avoiding any process of discretization of differential equations, i.e. PDE-free formulation. To this end, we must analyse in more detail the discretization of time by highlighting the need to introduce a dual sub...

We analyze the application to elastodynamic problems of mixed finite element methods for elasticity with weakly imposed symmetry of stress. Our approach leads to a semidiscrete method which consists of a system of ordinary differential equations without algebraic constraints. Our error analysis, which is based on a new elliptic projection operator, applies to several mixed finite element spaces...

An algorithm is presented for the multiple crack problem in planar linear elastostatics. The algorithm has three important properties: it is stable, it is adaptive, and its complexity is linear. This means that high accuracy can be achieved and that large-scale problems can be treated. In a numerical example stress fields are accurately computed in a mechanically loaded material containing 10,0...

We consider elastic bodies in rigid rotation, both nonrelativistically and in special relativity. Assuming a body to be in its natural state in the absence of rotation, we prove the existence of solutions to the elastic field equations for small angular velocity.