In this work, geometrically nonlinear static bending analysis of sandwich beams with a porous core and two skins made functionally graded materials using mesh-free method is presented. The material types the face sheets beam are chosen so that continuity between layers guaranteed. governing equation including geometric nonlinearity established via principle virtual work. This discretized into s...

The solution of time fractional partial differential equations in general exhibit a weak singularity near the initial time. In this article we propose method for solving diffusion equation with nonlocal term. proposed comprises L1 scheme on graded mesh, finite element and Newton’s method. We discuss well-posedness formulation at discrete level derive priori error estimates fully-discrete L2(Ω) ...

Let P be a polyhedral domain occupying a convex volume. We prove that the size of a graded mesh of P with bounded vertex degree is within a factor O(H P ) of the size of any Delaunay mesh of P with bounded radius-edge ratio. The term HP depends on the geometry of P and it is likely a small constant when the boundaries of P are fine triangular meshes. There are several consequences. First, among...

In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based TO for FRC use underlying finite element mesh both analysis design representation. This poses several limitations while enforcing sub-element spacing generating high-...

The main objective of this paper is to investigate the relations of rubber size, rubber content, and binder content in determination of optimum binder content for open graded friction course (OGFC). Mix gradation type B as specified in Specification for Porous Asphalt produced by the Road Engineering Association of Malaysia (REAM) was used in this study. Marshall specimens were prepared with fo...

Consider axisymmetric equations associated with Laplace-type operators. We establish full regularity estimates in high-order Kondrat′vetype spaces for possible singular solutions due to the non-smoothness of the domain and to the singular coefficients in the operator. Then, we show suitable graded meshes can be used in high-order finite element methods to achieve the optimal convergence rate, e...

Stacked layers of metal meshes embedded in a dielectric substrate are routinely used for providing spectral selection at THz frequencies. Recent work has shown that particular geometries allow the refractive index to be tuned to produce practical artificial materials. Here we show that by spatially grading in the plane of the mesh we can manufacture a Graded Index (GrIn) thin flat lens optimize...

Chew’s second Delaunay refinement algorithm with offcenter Steiner vertices leads to practical improvement over Ruppert’s algorithm for quality mesh generation, but the most thorough theoretical analysis is known only for Ruppert’s algorithm. A detailed analysis of Chew’s second Delaunay refinement algorithm with offcenters is given, improving the guarantee of well-graded output for any minimum...

We present a method for generating three-dimensional unstructured tetrahedral meshes of multi-material images. The method uses an octree as the background grid from which to build the final graded conforming meshes. The algorithm is fast and robust. It produces a small number of mesh elements and provides guaranteed bounds on the smallest dihedral angle and the two-sided Hausdorff distance betw...