Topic
Timoshenko beam theory
About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.
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TL;DR: In this paper, the snap-buckling behavior of functionally graded (FG) porous curved nanobeams resting on three parameters elastic foundations is studied for the first time, and it is shown that the buckling behavior is influenced by size effects, elastic foundations, geometry, material composition, porosity, and boundary conditions.
59 citations
TL;DR: In this paper, Eringen's equa- tions of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section.
Abstract: Buckling analysis of nanobeams is investigated using nonlocal continuum beam models of the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), and Levinson beam theory (LBT). To this end, Eringen's equa- tions of nonlocal elasticity are incorporated into the classical beam theories for buckling of nanobeams with rectangular cross-section. In contrast to the classical theories, the nonlocal elastic beam models developed here have the capability to predict critical buckling loads that allowing for the inclusion of size effects. The values of critical buckling loads corresponding to four commonly used boundary con- ditions are obtained using state-space method. The results are presented for different geometric parameters, boundary conditions, and values of nonlocal parameter to show the effects of each of them in detail. Then the results are fitted with those of molecular dynamics simulations through a nonlinear least square fitting procedure to find the appropriate values of nonlocal parameter for the buckling analy- sis of nanobeams relevant to each type of nonlocal beam model and boundary conditions.analysis. Based on the above introduction, it seems that size-effects consideration in the analysis of nanobeams is necessary. In this work, different nonlocal beam models corresponding to the different classical beam theories (22-24) are presented on the basis of Eringen's equations of nonlocal elasticity (25) to predict the buckling behavior of nanobeams with four com- monly used boundary conditions. State-space method is used to solve the governing differential equations for each type of nonlocal beam model with different boundary conditions. Various numerical results are given to show the influences of boundary conditions, aspect ratio, and values of nonlocal con- stant, separately. Then the results are matched with those of molecular dynamics simulations which are available in the literature to extract the correct values of nonlocal parameter corresponding to each type of nonlocal beam model and boundary conditions.
59 citations
TL;DR: In this article, an analytical estimation of voltage production of a piezoelectric cantilever beam when subjected to base excitation, with and without attached proof masses, is presented.
59 citations
TL;DR: An efficient formulation for dynamic analysis of planar Timoshenko's beam with finite rotations is presented in this paper, where both an inertial frame and a rotating frame are introduced to simplify computational manipulation.
59 citations
TL;DR: In this paper, a finite element formulation for Timoshenko beam element with only displacement degrees of freedom is first addressed for the laminated composite beams, and the resulting continuous isoparametric quadrilateral element is simple to formulate and efficient through the convergence with coarse meshes along the crack tip.
59 citations