Forced vibrations of functionally graded annular and circular plates by domain-boundary element method

Eshraghi, Iman
Dağ, Serkan
Axi-symmetric dynamic response of functionally graded circular and annular Mindlin plates with through-the-thickness variations of physical properties is investigated by a new domain-boundary element formulation. Three governing partial differential equations of motion of the inhomogeneous plate are converted to integral equations by utilizing the static fundamental solutions of the displacement components. These integral equations are then spatially discretized by dividing the entire domain into a number of cells and incorporating suitable shape functions to approximate the variation of unknown parameters across the cells. The resulting set of ordinary differential equations in time are then solved by the Houbolt method. To verify the accuracy of the developed procedure, dynamic responses generated for a homogeneous plate are compared to those calculated through an analytical solution. Different loading conditions such as step, harmonic, and impulsive loadings are considered for generation of numerical results of dynamic responses of functionally graded circular and annular plates. Convergence characteristics and effects of material inhomogeneity, and geometric parameters are extensively investigated. It has been shown that the presented method is a fast and accurate and technique in elastodynamic analysis of functionally graded plates.


GAMER, U; TEKKAYA, AE (1989-01-01)
Subject of this paper is the quasi-analytical treatment of the elastic-plastic spherical shell whose inner surface is heated slowly. The hardening behavior of the material is presumed isotropic, but it need not be specified beyond that. A first plastic region forms at the inner surface, and, for not too thick-walled shells, a second plastic region appears at the outer surface. The general results are specialized to linear hardening and thereafter to Swift's hardening law with the power one half. Numerical r...
Fracture mechanical behaviour of visco-elastic materials: application to the so-called dwell-effect
NAESER, Bastian; KALISKE, Michael; Dal, Hüsnü; NETZKER, Christiane (Wiley, 2009-08-01)
The material force approach is an efficient, elegant, and accepted means to compute the J-integral as a fracture mechanical parameter for elastic and inelastic materials. With the formulation of a multiplicative split of the deformation gradient at hand, rate-dependent (visco-elastic) materials described for example by the physically based Bergstrom-Boyce model can be investigated. For these investigations, the so-called material volume forces have to be computed in order to separate the driving forces acti...
Stress distributions in elastic-plastic rotating disks with elliptical thickness profiles using Tresca and von Mises criteria
Eraslan, Ahmet Nedim (Wiley, 2005-04-01)
Analytical and numerical solutions for the elastic-plastic stress distribution in rotating variable thickness solid and annular disks are obtained under plane stress assumption. The thickness of the disk is assumed to vary radially in elliptic form which represents a wide range of continuously variable nonlinear cross-sectional profiles. Tresca's yield criterion and its associated flow rule are used to obtain analytical solutions for a linear hardening material. A computational model is developed to obtain ...
Modeling of dislocation-grain boundary interactions in a strain gradient crystal plasticity framework
ÖZDEMİR, İZZET; Yalçınkaya, Tuncay (Springer Science and Business Media LLC, 2014-08-01)
This paper focuses on the continuum scale modeling of dislocation-grain boundary interactions and enriches a particular strain gradient crystal plasticity formulation (convex counter-part of Yal double dagger inkaya et al., J Mech Phys Solids 59:1-17, 2011; Int J Solids Struct 49:2625-2636, 2012) by incorporating explicitly the effect of grain boundaries on the plastic slip evolution. Within the framework of continuum thermodynamics, a consistent extension of the model is presented and a potential type non-...
Tezer, Münevver; ARIEL, PD (Wiley, 1988-01-01)
Flow of viscous, incompressible, electrically conducting fluid, driven by imposed electric currents has been investigated in the presence of a transverse magnetic field. The boundary perpendicular to the magnetic field is perfectly conducting partly along its length. Three cases have been considered: a) flow in the upper half plane when the boundary to the right of origin is insulating and that to the left is perfectly conducting, b) flow in the upper half plane when a finite length of the boundary is perfe...
Citation Formats
I. Eshraghi and S. Dağ, “Forced vibrations of functionally graded annular and circular plates by domain-boundary element method,” ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, pp. 0–0, 2020, Accessed: 00, 2020. [Online]. Available: