Structural symmetry within nonlocal integral elasticity: theoretical issues and computational strategies

Abstract

The structural symmetry and the appropriate definition of a reduced (symmetric) mechanical/ numerical model is discussed within a nonlocal elasticity context. In particular, reference is made to an integral model of Eringen-type. The paper highlights how the classical, i.e. local, concepts of structural symmetry have to be rephrased through the definition of an enlarged symmetric model of the analyzed structure. This enlarged model, endowed with apposite nonlocal boundary conditions enforced in an iterative fashion, is proved to be able to recover the nonlocal effects that the neglected portion of the structure exerts on the portion chosen for the analysis. It is shown how the mirrored symmetric solution exactly matches the complete one. Theoretical issues and computational strategies referred to a nonlocal version of the finite element method are discussed with reference to the analysis of a case-study.

Keywords

• Structural symmetry
• Nonlocal integral elasticity
• Nonlocal finite element method
• Enlarged symmetric model
• Nonlocal boundary conditions