The resolve of many important problems in practice that arise modern technology cannot always be obtained by traditional methods analytic function theory or means integral transformations. This applies, for example, to contact problems, which take into account the finite size region at least one direction, investigate environments with curvilinear anisotropy and like. mathematical elasticity ar...

Starting from a general classical model of many interacting particles we present well defined step by procedure to derive the continuum-mechanics equations nonlinear elasticity theory with fluctuations which describe macroscopic phenomena solid crystal. As relevant variables specify coarse-grained densities conserved quantities and properly displacement field describes local translations, rotat...

A new quasi-three-dimensional (3D) shear deformation theory, called the spectral displacement formulation (SDF), is proposed for high-precision static bending analyses of functionally graded plates. The main idea to expand unknown fields into Chebyshev series a unique form in thickness direction; truncation numbers are set be adjustable meet various application requirements. Specifically, 3D el...

In this paper a composite plate with similar unidirectional fibers is considered. Assuming orthotropic structure, theory of elasticity is used for investigating the stress concentration. Also, complex variable functions are utilized for solving the plane stress problems. Then the effective characteristics of this plate are studied numerically by using ANSYS software. In this research a volume e...

A generalized theory of elasticity, taking into account the rotational degrees of freedom of point bodies constituting a continuum, was proposed at the beginning of the twentieth century by the Cosserat brothers. We report the experimental observation of coupled rotational-translational modes in a noncohesive granular phononic crystal. While absent in the classical theory of elasticity, these e...