Strain gradient elasticity theory and its application to lattice beam structures

Keywords

Strain gradient elasticity, beam model, isogeometric analysis, lattice structure

Abstract

This paper investigates the bending behavior of beams by considering: (1) the Euler-Bernoulli beam model, (2) Mindlin’s strain gradient elasticity theory, (3) the von Kármán strain assumptions. The principle of virtual work is used to derive the non-linear governing equations in form of a six-order partial differential equation. A conforming Galerkin method based on an isogeometric approach is adopted to naturally fulfill a stringent C2continuity required by the present beam model. Thereafter, an application to lattice frame structures illustrates the benefits of the present beam model in saving computational costs while maintaining high accuracy as compared to standard 2D finite element simulations.

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