Elastodynamics and Elastostatics by a Unified Method of Potentials for x 3 -Convex Domains Morteza Eskandari-Ghadi & Ronald Y. S. Pak Received: 3 July 2007 / Accepted: 11 February 2008 / Published online: 14 March 2008 # Springer Science + Business Media B.V. 2008 Abstract A new general solution in terms of two scalar potential functions for classical elastodynamics of x 3 -convex domains is presented. Through the establishment and usage of a set of basic mathematical lemmas, a demonstration of its connection to Kovalevshi– Iacovache–Somigliana elastodynamic solution, and thus its completeness, is realized with the aid of the theory of repeated wave equations and Boggio’ s theorem. With the time dependence of the potentials suppressed, the new decomposition can, unlike Lamé’ s, degenerate to a complete solution for elastostatic problems. Keywords Dynamics . Statics . Elasticity . Displacement potentials . Completeness . Wave propagation . Solid mechanics Mathematics Subject Classification 74B05 . 74J05 1 Introduction The three-dimensional classical theory of elasticity has long been recognized as a foundation for advanced mechanics because of its sound mathematical framework and diverse practical utility. As an effective way to circumvent the difficulty in dealing with the coupled Navier ’ s equations, the method of potentials has played a major role in the solution of many complex initial-boundary value problems. Some of the most noteworthy potential functions are the Boussinesq potential, Galerkin vector, Helmholtz–Lamé potential functions, Love strain function, Papkovich-Neuber solution and Kovalevshi–Iacovache– J Elasticity (2008) 92:187–194 DOI 10.1007/s10659-008-9156-2 M. Eskandari-Ghadi Department of Engineering Science, Faculty of Engineering, University of Tehran, P.O. Box 11155-4563, Tehran, Iran e-mail: ghadi@ustmb.ut.ac.ir R. Y. S. Pak(*) Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, CO 80309-0428, USA e-mail: pak@colorado.edu