Vibration of thin elastic FGM plates with multi-gradation effects

In this paper we investigate the vibration response of thin elastic FGM plates with combination of transversal and/or in-plane gradation of various material parameters subjected to transient tension loading. The equations of motion and initial-boundary conditions for transient problems are derived within Kirchhoff-Love plate theory. For numerical modelling of plates with dynamic multi-gradation coupling effects, it is developed the strong formulation with using the meshless approximation of field variables by the Moving Least Square (MLS) approximation scheme. Several numerical examples are presented for illustration of the multi-gradation coupling effects in vibration response of elastic FGM plates

A Strong Form Meshless Method for the Solution of FGM Plates

Laminated composite structures suffer from failure because of concentrations of gradient fields on interfaces due to discontinuity of material properties. The rapid development of material science enables designers to replace classical laminated plate elements in aerospace structures with more advanced ones made of functionally graded materials (FGM), which are microscopic composite materials with continuous variation of material coefficients according to the contents of their micro-constituents. Utilization of FGM eliminates the inconvenience of laminated structures but gives rise to substantial changes in structural design This paper deals with the presentation of a strong formulation meshless method for the solution of FGM composite plates. Recall that the fourth-order derivatives of deflections are involved in the governing equations for plate structures. However, the high-order derivatives of field variables in partial differential equations (PDE) lead to increasing inaccuracy of approximations. For that reason, the decomposition of the high-order governing equations into the second-order PDE is proposed. For the spatial approximation of field variables, the meshless moving least square (MLS) approximation technique is employed. The reliability (numerical stability, convergence, and accuracy) as well as computational efficiency of the developed method is illustrated by several numerical investigations of the response of FGM plates with the transversal gradation of material coefficients under stationary and/or transient mechanical and thermal loadings

Thermo-electro-mechanical behaviour of Nano-sized structures

Thermo-electro-mechanical behaviour of the nano-sized structures is analysed by the finite element method (FEM). The mechanical response of the nano-sized structures cannot be modelled with classical continuum theories due to the size effect phenomenon. The strain gradient theory with one length scale parameter has been applied to study size effect phenomenon. The coupled theory of thermo-electricity has been used together with strain gradient theory of elasticity. The governing equations have been derived and incorporated into the commercial software Comsol via weak form module. The influence of the length scale parameter on mechanical response of the structures is investigated by some numerical examples

Thermo-electro-mechanical behaviour of Nano-sized structures

Thermo-electro-mechanical behaviour of the nano-sized structures is analysed by the finite element method (FEM). The mechanical response of the nano-sized structures cannot be modelled with classical continuum theories due to the size effect phenomenon. The strain gradient theory with one length scale parameter has been applied to study size effect phenomenon. The coupled theory of thermo-electricity has been used together with strain gradient theory of elasticity. The governing equations have been derived and incorporated into the commercial software Comsol via weak form module. The influence of the length scale parameter on mechanical response of the structures is investigated by some numerical examples

Transient analysis of FGM plates bending under thermal loading: comparative study within classical and generalized thermoelasticity

In the classical thermoelasticty, there is coupling between thermal and elastic fields, in general, but the elastic and thermal excitations spread according to physically different laws. In classical thermodynamics, the temperature change propagates according to diffusion law. However, the heat pulses at low temperature propagate evidently with a finite velocity in view of waves similar to spreading of elastic excitations. A great effort has been spent in this matter and there are two main non-classical theories: Lord-Shulman theory and Green-Lindsay theory. In this paper, we compare the response of thin FGM plates under thermal load within the classical and non-classical theories of thermoelasticity. The variable material properties of plate (such as the Young’s modulus, thermal expansion coefficient, etc.) are allowed to be continuous functions of the position. The strong form meshless formulations for solution of considered initial-boundary value problems is developed in combination with Moving Least Squares (MLS) approximation scheme. The response of FGM plates on thermal loading is studied via numerical simulations with focusing on comparison of results obtained within the classical and generalized thermoelasticity. The numerical results concern also the parametric study of influence of gradation of material coefficients on bending of FGM plate