Asymptotically Accurate Analytical Solution for Timoshenko-like Deformation of Functionally Graded Beams

IF 2.6 4区 工程技术 Q2 MECHANICS
Amandeep, Satwinder Singh, S. Padhee
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引用次数: 1

Abstract

A closed-form analytical solution is developed for a planar inhomogeneous beam subjected to transverse loading, using Variational Asymptotic Method (VAM). The VAM decouples the problem into a cross-sectional and an along-the-length analysis, leading to a set of ordinary differential equations. These equations along with associated boundary conditions have been solved to obtain the closed-form analytical solutions. Three distinct gradation models have been used to validate the present formulation against 3D FEA and few prominent results from the literature. Excellent agreement has been obtained for all the test cases. Key contributions of the present work are (a) the solutions have been obtained without any ad-hoc and a-prior assumptions (b) the ordered warping solutions results in Euler-Bernoulli type deformation in the zeroth-order, whereas the higher-order solutions provide novel closed-form expressions for transverse shear strain and stress. Finally, the effect of inhomogeneity on various field variables has been analyzed and discussed.
梯度梁类Timoshenko变形的渐近精确解析解
利用变分渐近法(VAM)得到了平面非均匀梁在横向荷载作用下的闭合解析解。VAM将问题解耦为截面分析和长度分析,从而得到一组常微分方程。这些方程以及相关的边界条件已经被求解,以获得闭合形式的解析解。三个不同的级配模型已被用于根据三维有限元分析和文献中的少数突出结果验证当前公式。所有测试用例都获得了极好的一致性。本工作的主要贡献是:(a)在没有任何特别和a先验假设的情况下获得了解;(b)有序翘曲解导致零阶欧拉-伯努利型变形,而高阶解提供了横向剪切应变和应力的新的闭合形式表达式。最后,分析和讨论了不均匀性对各种场变量的影响。
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来源期刊
CiteScore
4.80
自引率
3.80%
发文量
95
审稿时长
5.8 months
期刊介绍: All areas of theoretical and applied mechanics including, but not limited to: Aerodynamics; Aeroelasticity; Biomechanics; Boundary layers; Composite materials; Computational mechanics; Constitutive modeling of materials; Dynamics; Elasticity; Experimental mechanics; Flow and fracture; Heat transport in fluid flows; Hydraulics; Impact; Internal flow; Mechanical properties of materials; Mechanics of shocks; Micromechanics; Nanomechanics; Plasticity; Stress analysis; Structures; Thermodynamics of materials and in flowing fluids; Thermo-mechanics; Turbulence; Vibration; Wave propagation
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