Ahmad Shahba

TL;DR: In this article, the free vibration and stability analysis of axially functionally graded tapered Timoshenko beams is studied through a finite element approach, where exact shape functions for uniform homogeneous Timoshenko beam elements are used to formulate the proposed element.

TL;DR: In this paper, the free vibration and stability of axially functionally graded tapered Euler-Bernoulli beams were studied through solving the governing differential equations of motion. But, the convergence rate of the conventional differential transform method (DTM) does not necessarily converge to satisfactory results, and a new approach based on DTM called differential transform element method (DTEM) is introduced which considerably improves the convergence of the method.

TL;DR: In this paper, a beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements, and the effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices.

TL;DR: In this article, the authors developed a dislocation density-based crystal plasticity constitutive relation with a unified flow rule by combining the thermally-activated and drag-dominated stages of dislocation slip, suitable for modeling deformation at a wide range of strain-rates.

TL;DR: In this paper, a novel method based on mechanical/structural principles is introduced for free vibration analysis of arbitrarily tapered Timoshenko beams in preference to primarily mathematically based methodologies.