Finite Element Analyses of the Modified Strain Gradient Theory Based Kirchhoff Microplates

An Efficient Strain Based Cylindrical Shell Finite Element

The need for compatibility between degrees of freedom of various elements is a major problem encountered in practice during the modeling of complex structures; the problem is generally solved by an additional rotational degree of freedom [1-3]. This present paper investigates possible improvements to the performances of strain based cylindrical shell finite element [4] by introducing an additio...

Static analysis of rectangular nanoplates using exponential shear deformation theory based on strain gradient elasticity theory

In this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. For this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. From the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...

A Semi-analytical Solution for Flexural Vibration of Micro Beams Based on the Strain Gradient Theory

In this paper, the flexural free vibrations of three dimensional micro beams are investigated based on strain gradient theory. The most general form of the strain gradient theory which contains five higher-order material constants has been applied to the micro beam to take the small-scale effects into account. Having considered the Euler-Bernoulli beam model, governing equations of motion are w...

Geometrically Exact Finite Element Formulations for Curved Slender Beams: Kirchhoff-Love Theory vs. Simo-Reissner Theory

The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and SimoReissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak...

An Algorithm for Finite Element Analysis of Tunnel Supports Based on the Winkler’s Theory