On Representing Strain Gradient Elastic Solutions of Boundary Value Problems by Encompassing the Classical Elastic Solution

Antonios Charalambopoulos, Theodore Gortsas and Demosthenes Polyzos
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Antonios Charalambopoulos: School of Applied Mathematics and Physical Sciences, National Technical University of Athens, 15780 Athens, Greece
Theodore Gortsas: Department of Mechanical Engineering and Aeronautics, University of Patras, 26504 Patras, Greece
Demosthenes Polyzos: Department of Mechanical Engineering and Aeronautics, University of Patras, 26504 Patras, Greece

Mathematics, 2022, vol. 10, issue 7, 1-22

Abstract: The present work aims to primarily provide a general representation of the solution of the simplified elastostatics version of Mindlin’s Form II first-strain gradient elastic theory, which converges to the solution of the corresponding classical elastic boundary value problem as the intrinsic gradient parameters become zero. Through functional theory considerations, a solution representation of the one-intrinsic-parameter strain gradient elastostatic equation that comprises the classical elastic solution of the corresponding boundary value problem is rigorously provided for the first time. Next, that solution representation is employed to give an answer to contradictions arising by two well-known first-strain gradient elastic models proposed in the literature to describe the strain gradient elastostatic bending behavior of Bernoulli–Euler beams.

Keywords: strain gradient elastic theory; general solution representation; Bernoulli–Euler beam; material with microstructure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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