We present general, computable, improvable, and rigorous bounds for the total energy of a finite heterogeneous volume element O or a periodically distributed unit cell of an elastic composite of any known distribution of inhomogeneities of any geometry and elasticity, undergoing a harmonic motion at a fixed frequency or supporting a singlefrequency Bloch-form elastic wave of a given wavevector....

We propose a variational h-adaption strategy in which the evolution of the mesh is driven directly by the governing minimum principle. This minimum principle is the principle of minimum potential energy in the case of elastostatics; and a minimum principle for the incremental static problem of elasto-viscoplasticity. In particular, the mesh is refined locally when the resulting energy or increm...

We use symmetric smoothed particle hydrodynamics (SSPH) and moving least squares (MLS) basis functions to analyze six linear elastostatics problems by first deriving their Petrov-Galerkin approximations. With SSPH basis functions one can approximate the trial solution and its derivatives by using different basis functions whereas with MLS basis functions the derivatives of the trial solution in...

The hybrid boundary element method, a variational formulation introduced in 1987 by the first author, has proven to be a powerful tool for dealing with a great variety of problems of potential, elastostatics and elastodynamics. One of the most recent endeavors of the research team at PUC-Rio is the application of the method to problems of the linear elastic fracture mechanics. In the M.Sc. diss...

This paper is concerned with the hp-version of the finite element method (hp-FEM) to treat a variational inequality that models frictional contact in linear elastostatics. Such an approximation of higher order leads to a nonconforming discretization scheme. We employ Gauss-Lobatto quadrature for the approximation of the nonsmooth frictiontype functional and take the resulting quadrature error i...