Abstract: A method for determining the stress distribution of a rectangular plate subjected to two pairs of arbitrarily distributed in-plane edge shear loads is proposed, and the free vibration and buckling of such a rectangular plate are investigated in this work. The method utilizes two stress functions to synthesize the stress-resultant field of the plate with each of the stress functions satisfying the biharmonic compatibility equation. The sum of stress-resultant fields due to these two stress functions satisfies the boundary conditions at the edges of the plate, from which these two stress functions are determined. Then, the free vibration and buckling of the rectangular plate are investigated by the Galerkin method. Numerical results obtained by this work are compared with those appeared in the literature, and good agreements are observed.
Abstract: In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.
Abstract: The Wavelet-Galerkin finite element method for
solving the one-dimensional heat equation is presented in this work.
Two types of basis functions which are the Lagrange and multi-level
wavelet bases are employed to derive the full form of matrix system.
We consider both linear and quadratic bases in the Galerkin method.
Time derivative is approximated by polynomial time basis that
provides easily extend the order of approximation in time space. Our
numerical results show that the rate of convergences for the linear
Lagrange and the linear wavelet bases are the same and in order 2
while the rate of convergences for the quadratic Lagrange and the
quadratic wavelet bases are approximately in order 4. It also reveals
that the wavelet basis provides an easy treatment to improve
numerical resolutions that can be done by increasing just its desired
levels in the multilevel construction process.