Exact solution for size-dependent elastic response in laminated beams considering generalized first strain gradient elasticity

Abstract

In this paper, exact solutions for the static bending response of laminated composite beams have been derived considering the effect of strain gradient elasticity. Separate solutions for the laminate comprising of isotropic and orthotropic laminae have been presented here. The sixth-order tensor for the higher order elastic coefficients has been evaluated using the generalized first strain gradient elasticity model with three independent material length constants. The significance of the gradient elasticity in low-dimensional structures has been established employing numerical examples of micro and nano-beams, and comparing the current results with the classical elasticity results. A parametric study over the variation of the axial, transverse Cauchy and physical stresses across the thickness of the beam has been conducted. Also, the discontinuity of the inter-laminar transverse Cauchy stresses and higher order stresses across the thickness has been studied in the current framework. The exact solutions developed in this paper may be used as benchmark results for validating further research involving the strain gradient elastic response of low-dimensional laminated composite beams.