Solution of plane transient elastodynamic problems by finite elements and laplace transform

The general transient linear elastodynamic problem under conditions of plane stress or plane strain is numerically solved by a special finite element method combined with numerical Laplace transform. A rectangular finite element with eight degrees of freedom is constructed on the basis of the governing equations of motion in the Laplace transformed domain. Thus the problem is formulated and numerically solved in the transformed domain and the time domain response is obtained by a numerical inversion of the transformed solution. Viscoelastic material behavior is easily taken into account by invoking the correspondence principle. The method appears to have certain advantages over conventional finite element techniques.