Monte Carlo Based Isogeometric Stochastic Finite Element Method for Uncertainty Quantization in Vibration Analysis of Piezoelectric Materials

Free Vibration Analysis of Nanoplates Made of Functionally Graded Materials Based On Nonlocal Elasticity Theory Using Finite Element Method

In this paper, an analysis of free vibration in functionally graded nanoplate is presented. Third-order shear deformation plate theory is used to reach more accuracy in results. Small-scale effects are investigated using Eringen`s nonlocal theory. The governing equations of motion are obtained by Hamilton`s principle. It is assumed that the properties of nanoplates vary through their thicknesse...

Multi-Level Monte Carlo Finite Element Method for Elliptic Partial Differential Equations with Stochastic Data

Multi-level Monte Carlo Finite Element method for elliptic PDEs with stochastic coefficients

It is a well–known property of Monte Carlo methods that quadrupling the sample size halves the error. In the case of simulations of a stochastic partial differential equations, this implies that the total work is the sample size times the discretization costs of the equation. This leads to a convergence rate which is impractical for many simulations, namely in finance, physics and geosciences. ...

Mixed finite element formulation enriched by Adomian method for vibration analysis of horizontally curved beams

Abstract: The vibration analysis of horizontally curved beams is generally led to higher order shape functions using direct finite element method, resulting in more time-consuming computation process. In this paper, the weak-form mixed finite element method was used to reduce the order of shape functions. The shape functions were first considered linear which did not provide adequate accuracy....

Finite Element Analysis of Functionally Graded‎ ‎Piezoelectric Beams

In this paper‎, ‎the static bending‎, ‎free vibration‎, ‎and dynamic response of functionally graded‎ ‎piezoelectric beams have been carried out by finite element method‎‎under different sets of mechanical‎, ‎thermal‎, ‎and electrical‎ ‎loadings‎. ‎The beam with functionally graded piezoelectric material‎ ‎(FGPM) is assumed to be graded across the thickness with a simple‎ ‎power law distributio...