Two-phase local/nonlocal mixture models for buckling analysis of higher-order refined shear deformation beams under thermal effect

Abstract

In this paper, we study the well-posedness of various nonlocal integral theories for formulating predictive models of buckling of higher-order refined shear deformation beams. We find that the two popular purely nonlocal models (i.e., strain- and stress-driven strategies) are ill-posed for the problem at hand. As a remedy, their corresponding two-phase local/nonlocal mixture formulations are well-posed for the problem. Numerical results, obtained by the generalized differential quadrature method (GDQM), show that the strain- and stress-driven local/nonlocal mixture model can predict consistent softening and stiffening effects, respectively. Moreover, the two-phase nonlocal influence on the thermal loads is also investigated.

Keywords:

• Local/nonlocal mixture models
• buckling loads
• higher-order refined beam theory
• two-phase thermal load
• GDQM

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (No. 12172169) and the Priority Academic Program Development of Jiangsu Higher Education Institutions. Zhang appreciates the China Scholarship Council (CSC) for supporting his joint training (No. 202006830038) at the University of Alberta. Schiavone acknowledges the support of the Natural Sciences and Engineering Research Council of Canada via a Discovery Grant (Grant No: RGPIN – 2017 - 03716115112).