The performance of finite element computation depends strongly on the quality of the geometric mesh and the efficiency of the numerical solution of the linear systems resulting from the discretization of partial differential equation (PDE) models. It is common knowledge that mesh geometry affects not only the approximation error of the finite element solution but also the spectral properties of...

A new method is presented for identifying the local stiffness of a structure from vibration test data. The method is based on a projection of the experimentally measured flexibility matrix onto the strain energy distribution in local elements or regional superelements. Using both a presumed connectivity and a presumed strain energy distribution pattern, the method forms a well-determined linear...

We analyze and compare different techniques to set up the stiffness matrix in the hp-version of the finite element method. The emphasis is on methods for second order elliptic problems posed on meshes including triangular and tetrahedral elements. The polynomial degree may be variable. We present a generalization of the Spectral Galerkin Algorithm of [7], where the shape functions are adapted t...

We study the preconditioning of the stiffness matrix which arises from the discretization of the Poisson equation using IsoGeometric Method (IGM). A study of condition number of stiffness matrices, resulting from NURBS based IGM, suggests that novel preconditioning techniques are needed for fast and efficient iterative solvers for the resulting linear system. As a first step towards preconditio...

In this paper, bending analysis of concentric and eccentric beam stiffened square and rectangular plate using the meshless collocation method has been investigated. For detecting the governing equations of plate and beams, Mindlin plate theory and Timoshenko beam theory have been used, respectively, with the stiffness matrices of the plate and the beams obtained separately. The stiffness matric...

This article deals with the efficient (approximate) inversion of finite element stiffness matrices of general second-order elliptic operators with L∞-coefficients. It will be shown that the inverse stiffness matrix can be approximated by hierarchical matrices (H-matrices). Furthermore, numerical results will demonstrate that it is possible to compute an approximate inverse with almost linear co...

Due to the mismatch of mechanical properties in composite laminates, propagation of delami-nation is considered as a severe damage mechanism in beams with various lay-up configurations. Delamination can be generated due to matrix cracking propagation or it can also be initiated due to the manufacturing process before using composite beams. Using a micromechanics model, this study is aimed to in...

This study explored the free vibration problem in relation to glass fiber reinforced polymer (GFRP) plates with central cutouts and free boundaries using theoretical, experimental, and numerical methods. The theoretical formulations were derived from the classical lamination plate theory. The rectangular cutout was mathematically modeled into the stiffness matrix of the plate by multiplying Hea...

How must n equal circles of given radius be placed so that they cover as great a part of the area of the unit circle as possible? To analyse this mathematical problem, mechanical models are introduced. A generalized tensegrity structure is associated with a maximum area configuration of the n circles, whose equilibrium configuration is determined numerically with the method of dynamic relaxatio...