Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary con-How to cite this paper: Surana, K.S. and Alverio, E.N. (2020) Consistency and Validity of the Mathematical Models and the Solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and
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