A Study of the Correspondence Rule in a Viscoelastic Stress Analysis

Abstract

This thesis is mainly concerned with two fields of investigation; the viscoelastic behaviour of plastics, and the numerical solution of engineering problems by means of finite element methods. The basic equations describing linear elastic behaviour are modified to give corresponding equations for linear viscoelastic materials, and various theoretical models are used to describe viscoelastic behaviour. The stiffness matrix for a tapered element of a beam is derived for cases where the shear stress is neglected and where its effect is allowed for, and S melebee solutions are obtained for various bending problems. Bending is also considered as a plane stress problem, using triangular elements. By combining the results obtained from linear viscoelastic theory and finite element methods theoretical solutions are obtained for a number of more difficult viscoelastic problems, and the results are compared with those obtained by experiment. Theoretical and experimental results are also given for certain non-linear viscoelastic problems. Finally methods of designing in plastics are discussed in relation to the results previously obtained. Throughout, extensive use is made of computer solutions, and the development of the programs is detailed in the Appendix