Static and Dynamic Analysis of Strain Gradient Planar Trusses

Abstract

This paper examines the static and dynamic responses of strain gradient planar trusses. Classical elasticity (CE) theory lacks a material microstructural length parameter in its governing equations, making it insufficient to capture size-dependent effects. To address this limitation, higher-order continuum theories—such as micropolar, couple-stress, and strain gradient elasticity (SGE) theories—are essential. In this study, gradient elasticity theory is extended to describe the behavior of planar trusses by incorporating explicit internal length scales as additional material parameters. A key finding of this research is that the inclusion of the microstructural parameter results in a stiffening effect in both static and dynamic analyses.

Keywords

• strain gradient elasticity
• finite element method
• exact stiffness matrix
• exact mass matrix
• planar trusses
• eigenvalues