N. Valizadeh

Bio: N. Valizadeh is an academic researcher from Bauhaus University, Weimar. The author has contributed to research in topics: Isogeometric analysis & Finite element method. The author has an hindex of 11, co-authored 22 publications receiving 1363 citations. Previous affiliations of N. Valizadeh include Shahid Bahonar University of Kerman.

Extended isogeometric analysis for simulation of stationary and propagating cracks

Abstract: SUMMARY A novel approach based on a combination of isogeometric analysis (IGA) and extended FEM is presented for fracture analysis of structures. The extended isogeometric analysis is capable of an efficient analysis of general crack problems using nonuniform rational B-splines as basis functions for both the solution field approximation and the geometric description, and it can reproduce crack tip singular fields and discontinuity across a crack. IGA has attracted a lot of interest for solving different types of engineering problems and is now further extended for the analysis of crack stability and propagation in two-dimensional isotropic media. Concepts of the extended FEM are used in IGA to avoid the necessity of remeshing in crack propagation problems and to increase the solution accuracy around the crack tip. Crack discontinuity is represented by the Heaviside function and isotropic analytical displacement fields near a crack tip are reproduced by means of the crack tip enrichment functions. Also, the Lagrange multiplier method is used to impose essential boundary conditions. Moreover, the subtriangles technique is utilized for improving the accuracy of integration by the Gauss quadrature rule. Several two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method and the results of mixed-mode stress intensity factors are compared with analytical and extended FEM results. Copyright © 2011 John Wiley & Sons, Ltd.

Introduction to the Finite Element Method

Abstract: This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Dual‐horizon peridynamics

Abstract: Summary In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes The present formulation fulfills both the balances of linear momentum and angular momentum exactly Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue We will show that the traditional peridynamics can be derived as a special case of the present DH-PD All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes A simple adaptive refinement procedure is proposed, reducing the computational cost Both two-dimensional and three-dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method Copyright © 2016 John Wiley & Sons, Ltd