On the finite element formulation for second-order strain gradient nonlocal beam theories. Issue 15 (3rd August 2019)

• Record Type: Journal Article
• Authors: Babu, Bishweshwar; Patel, B. P.
• Is Part Of: Mechanics of advanced materials and structures. Volume 26:Issue 15(2019)
• Page Start: 1316
• Page End: 1332
• Publication Date: 2019-08-03
• Subjects: Nonlocal -- strain gradient -- finite element formulation -- analytical; Composite materials -- Mechanical properties -- Periodicals; Composite construction -- Periodicals; 620.118
• DOI: 10.1080/15376494.2018.1432807
• Languages: English
• ISSNs: 1537-6494

Abstract

ABSTRACT: Finite element (FE) formulation of nanobeams using second-order positive/negative strain gradient theories is presented. The variational statement for beam, written using Hamilton's principle involving virtual work of stress/moment resultants, with C 1 continuity requirement leads to unsymmetric nonlocal terms whereas the symmetrization of the nonlocal terms leads to C 2 continuity requirement. The C 2 continuous FE with proper boundary conditions is accurate for the modeling of nanobeams using second-order strain gradient theories. The negative strain gradient model predicts results matching with the experimental investigations on microbeams. The strain gradient theory based plate FE is also formulated by extending C 2 continuous beam FE formulation.