In this paper we will review and extend the results of [21], which covered the case of 3D thermo-piezoelectric polycrystals. In that context the settings of conductivity, elasticity, pyroelectricity, piezoelectricity, thermo-electricity and thermo-elasticity can be viewed as particular cases. We will consider a class of composites more general than polycrystals, where the set of allowable mater...

In this paper we will review and extend the results of [21], which covered the case of 3D thermo-piezoelectric polycrystals. In that context the settings of conductivity, elasticity, pyroelectricity, piezoelectricity, thermo-electricity and thermo-elasticity can be viewed as particular cases. We will consider a class of composites more general than polycrystals, where the set of allowable mater...

In this paper we apply the method developed by Rice [1], of solving for the elastic field of a crack with a front perturbed from some reference shape, to solve the elasticity problems of somewhat circular planar tensile cracks under arbitrary load distributions. The method is based on a known solution for the stress intensity factor along a circular crack due to a pair of wedge-opening point fo...

in this paper a new form of the homptopy perturbation method is used for solving oscillator differential equation, which yields the maclaurin series of the exact solution. nonlinear vibration problems and differential equation oscillations have crucial importance in all areas of science and engineering. these equations equip a significant mathematical model for dynamical systems. the accuracy o...

The Gradient Scheme framework provides a unified analysis setting for many different families of numerical methods for diffusion equations. We show in this paper that the Gradient Scheme framework can be adapted to elasticity equations, and provides error estimates for linear elasticity and convergence results for non-linear elasticity. We also establish that several classical and modern numeri...