Boundary element analysis of static plane problems in size-dependent consistent couple stress elasticity

2021 ◽  
Vol 132 ◽  
pp. 399-415
Author(s):  
Jun Lei ◽  
Pengsheng Ding ◽  
Chuanzeng Zhang
Keyword(s):  
Boundary Element ◽  
Couple Stress ◽  
Element Analysis ◽  
Size Dependent ◽  
Couple Stress Elasticity ◽  
Boundary Element Analysis ◽  
Static Plane

Boundary Element Analysis of Thermoelastic Effects in Size-Dependent Mechanics

2015 ◽  
Author(s):  
A. Hajesfandiari ◽  
A. R. Hadjesfandiari ◽  
G. F. Dargush
Keyword(s):  
Boundary Element ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Characteristic Parameter ◽  
Boundary Integral ◽  
Element Formulation ◽  
Length Scale ◽  
Numerical Implementation ◽  
Element Analysis ◽  
Size Dependent

A new boundary element formulation is developed to analyze two-dimensional size-dependent thermoelastic response in linear isotropic couple stress materials. The model is based on the recently developed consistent couple stress theory, in which the couple-stress tensor is skew-symmetric. The size-dependency effect is specified by one characteristic parameter length scale l, while the thermal effect is quantified by the classical thermal expansion coefficient α and conductivity k. We discuss the boundary integral formulation and numerical implementation of this size-dependent thermoelasticity boundary element method (BEM). Then, we apply the resulting BEM formulation to a computational example to validate the numerical implementation and to explore thermoelastic couplings as the non-dimensional characteristic scale of the problem is varied. Interestingly, for a cantilever beam with a transverse temperature gradient, we find significantly reduced non-dimensional tip deflections as the beam depth h approaches the material characteristic length scale l. On the other hand, when l/h < 0.01, the classical size-independent deflections are recovered.

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