Numerical solutions obtained by the Meshless Local Petrov-Galerkin (MLPG) method are presented for static deformations, free and forced vibrations of a functionally graded (FG) cantilever beam. The MLPG method is a truly meshless approach, as it does not need any background mesh for integration in the weak form. In this MLPG method, an orthogonal transformation technique is used to enforce nodal variables directly in the essential boundary areas, and the test function is chosen to equal the weight function of the moving least squares approximation. The cantilever beam, made of two isotropic constituents, is assumed to be macroscopically isotropic and to have a power-law variation proportional to the volume fractions of the constituents in the thickness and the longitudinal directions. Effective material moduli at a material point are computed with the Mori-Tanaka homogenization technique. Computed results for static, free and forced vibration analyses are found to agree well with their corresponding finite element solutions. Different volume fractions of material constituents on the performance and response of FG beams are also investigated.

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Thermomechanical deformation of a functionally graded composite (FGC) in elevated temperature environments is investigated by the meshless local Petrov-Galerkin method. The FGC is modeled as a 2-D linearly elastic solid which consists of ceramic ZrO 2 and alloy Ti-6Al-4V with the volume fraction varying along a predefined direction. Unlike most investigations performed so far, temperature-dependent thermophysical and thermomechanical properties are considered for both constituents in this work. The effective material properties of the FGC are evaluated with the micromechanical models. An FGC hollow cylinder under an internal temperature change is first studied; the numerical results agree very well with those computed by the finite element method. The parametric studies with respect to different profiles of graded FGCs are performed for a clamped-clamped thick beam and a square plate with a central hole, respectively. It is found that inclusion of temperature dependence for the material properties has a great impact on thermomechanical response prediction for FGCs in elevated temperature environments.

We investigate shock-induced detonation of high explosives confined in an open-ended steel cylinder by a normal impact to the cylindrical surface using three-dimensional finite element analysis. Three types of steel projectiles are considered: a cube, a sphere and a square plate. For the encased LX-17 explosive the calculated threshold impact velocities that lead to deflagration and detonation are higher for a sphere than for a cube of the same mass. It is found that detonation of the encased PBXN-110 explosive with the cubical projectile could occur immediately once a full reaction is initiated in the region near the impact site. The threshold detonation velocity is much lower for PBXN-110 than for LX-17. In addition, we discuss the threshold conditions of detonation predicted by different equations of state and failure models for the steel casing and projectile.