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

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