Narrow Results

In this paper, on the basis of gradient elasticity theory with one gradient parameter, wave propagation in rectangular nanoplates is studied. In the governing equation, the influences of initial stresses and elastic foundation are also considered. An analytical approach is used to solve the governing equation. The effects of different parameters such as gradient parameter on the circular and cut-off frequencies are presented. One can see that the initial stress and gradient parameter play an important role in investigating the wave propagation in nanoplates.

Bi-modulus materials exhibit the different modulus in tension and compression. The value of elastic modulus and Poisson ratio of every point in the bi-modulus elastic body not only depend on the material itself, but also the stress state and the strain state of the point. The uncertainty and nonlinearity of the elastic constitutive relation result in that the bi-modulus elastic problem is the complicated nonlinear problem This paper aims at studying the bi-modulus elastic constitutive equation employed in the bi-modulus finite element numerical method (FEM). The new elastic matrix model is proposed based on Ye’s principal strain criterion with the assumption that the Poisson ratio maintain constant whenever in tension or in compression, and the elastic matrix is symmetric by equivalent transmitting. The shear modulus expression of this elastic matrix model is derived to enable the elastic matrix completely and improve the convergence of the FEM calculation. The statically indeterminate bi-modulus beam is analyzed by means of FEM employing the proposed elastic matrix model. The effects of the tensile modulus to compressive modulus ratio and the boundary condition on the stress and deflection of the bi-modulus beam is studied.