During the last ten years, various meshless techniques have been developed to solve complex boundary value problems. However, there is still not yet an efficient meshless method available for general linear static analysis. The method of finite spheres is a promising meshless technique with respect to efficiency and applicability [1]. In this paper, improvements of the method of finite spheres ...

Engineering mechanics formulations of aerospace industry problems overwhelmingly rely upon spatial averaging techniques. Crucial applications in the area of dynamic response analysis and stochastic estimation of material degradation can be cited as important cases. Integration procedures on finite domains underlie physically acceptable averaging processes. Unlike one-dimensional cases, integral...

In the current work, we implement the meshless local radial point interpolation (MLRPI) method to find numerical solution of one-dimensional linear telegraph equations with variable coefficients. The MLRPI method, as a meshless technique, does not require any background integration cells and all integrations are carried out locally over small quadrature domains of regular shapes, such as lines ...

In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the n-dimensional hypersurface, Γ ⊂ Rn+1, is embedded in a polyhedral domain in Rn+1 consisting of a union, Th, of (n+ 1)-simplices. The unifying feature of the methodological approach is that the finit...

Given an unsteady flow field, one common way to compute Lagrangian Coherent Structures (LCS) is to extract extremal structures of the Finite Time Lyapunov Exponent (FTLE). Experience has shown that the resulting structures are often close to material structures (i.e., material lines or material surfaces). Moreover, it has been proven that for an integration time converging to infinity, they con...

A Finite Element Analysis (FEA) system was designed for the analysis of creep deformation and damage evolution in weldment. This project essentially consists of three parts which involves 1) transfer programme development, 2) numerical integration subroutine development, and 3) validation of complete FEA system. Firstly, the development of a user-friendly preand postprocessing transfer programm...

We derive an analytic expression for the scalar one-loop pentagon and hexagon functions which is convenient for subsequent numerical integration. These functions are of relevance in the computation of next-to-leading order radiative corrections to multi-particle cross sections. The hexagon integral is represented in terms of n-dimensional triangle functions and (n+2)dimensional box functions. I...

Using numerical integration in the formulation of the finite-element geometric stiffness matrix and placing movable nodes at integration points causes the geometric stiffness matrix to become lumped or diagonal. The consistent geometric stiffness matrix which is a non-diagonal matrix, is normally used in the finite-element eigenvalue buckling problem. Altering the method to deliver a diagonal (...

The communication presents numerical results in the form of a comparison of predictions due to a numerical algorithm using a previously published exact nonlocal Absorbing Boundary Condition (ABC) and analytical results for the field radiated by an infinitely small dipole. The numerical approximations are derived, and application to the FDTD method is straightforward. The method is compared to a...