On the application of the partition of unity method for nonlocal response of low-dimensional structures

Journal of the Mechanical Behavior of Materials

Natarajan Sundararajan¹ 

[1] Department of Mechanical Engineering, Indian Institute of Technology-Madras, Chennai 600036, India;

关键词: axial vibration;    euler-bernoulli beam;    extended finite element method;    flexural vibration;    gradient elasticity;    moving least-squares approximants;    nonlocal integral elasticity;    timoshenko beam;   

DOI  :  10.1515/jmbm-2014-0017

来源: DOAJ

【 摘 要 】

The main objectives of the paper are to (1) present an overview of nonlocal integral elasticity and Aifantis gradient elasticity theory and (2) discuss the application of partition of unity methods to study the response of low-dimensional structures. We present different choices of approximation functions for gradient elasticity, namely Lagrange intepolants, moving least-squares approximants and non-uniform rational B-splines. Next, we employ these approximation functions to study the response of nanobeams based on Euler-Bernoulli and Timoshenko theories as well as to study nanoplates based on first-order shear deformation theory. The response of nanobeams and nanoplates is studied using Eringen’s nonlocal elasticity theory. The influence of the nonlocal parameter, the beam and the plate aspect ratio and the boundary conditions on the global response is numerically studied. The influence of a crack on the axial vibration and buckling characteristics of nanobeams is also numerically studied.

【 授权许可】

Unknown