The aim of this study is to develop an algorithm for calculating rectangular plates statistical loads taking into account geometrical nonlinearity on the basis difference equations method sequential approximations full and partial contact with elastic base. For our study, we used methods: finite elements approximations, theory plate calculation considering large deflections. Results: a method, ...

An instantaneous sub-surface disturbance in a two-dimensional elastic half-space is considered. The propagates through the material until it reaches free surface, after which out along surface. In conventional theory, free-surface conditions on unknown surface are projected onto flat plane \(y = 0\), so that linear model may be used. Here, however, we present formulation takes explicit account ...

This paper studies a new approach to analyze the large deflection behavior of prismatic and non-prismatic beams of non-homogenous material under combined load and multiple boundary conditions. The mathematical formulation has been derived which led to a set of six first-order ordinary differential equations. The geometric nonlinearity was solved numerically using the multiple shooting method co...

In this letter, we describe the propagation of longitudinal waves in one-dimensional nonlinear elastic thin rods with material nonlinearity and geometric nonlinearity. Mathematical analysis is used to derive analytical dispersion relationship waves; subsequently, numerical Fourier spectrum method solve wave equation directly results are verify correctness derived relation.

A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a C2 function H to be the mean curvature of some conformal scalar flat metric is that H is positive somewhere. We show that, when the boundary is umbilic and the fu...

A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, a necessary and sufficient condition for a C2 function H to be the mean curvature of some conformal flat metric is that H is positive somewhere. We show that all such metrics stay in a compact set with res...