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: The first-order shear deformation beam theory for axially loaded rectangular functionally graded beams is developed in this article, where the improved transverse shear stiffness is derived from the in-plane stress and equilibrium equation and the associated shear correction factor is then obtained analytically.
Abstract: The first-order shear deformation beam theory for static and free vibration of axially loaded rectangular functionally graded beams is developed. In this theory, the improved transverse shear stiffness is derived from the in-plane stress and equilibrium equation and thus, associated shear correction factor is then obtained analytically. Equations of motion are derived from the Hamilton’s principle. Analytical solutions are presented for simply-supported functionally graded beams. The obtained results are compared with the existing solutions to verify the validity of the developed theory. Effects of the power-law index, material contrast and Poisson’s ratio on the displacements, natural frequencies, buckling loads and load–frequency curves as well as corresponding mode shapes are investigated.
131 citations
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TL;DR: In this paper, a beam of general (both symmetric and non-symmetric) cross-section is considered and three-dimensional static and dynamic information and results for a beam with homogeneous, isotropic beams are brought to bear on these issues.
131 citations
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TL;DR: In this paper, a soil-tunnel interaction model based on the Timoshenko beam simplified model (TBSM) of tunnel on Vlasov foundation was proposed to analyze the behaviors of a shield tunnel subjected to external forces transferred from surcharge load on the ground surface.
130 citations
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TL;DR: In this paper, the buckling analysis of three microbeam models based on modified couple stress theory is investigated, and a generalized differential quadrature (GDQ) method is employed to solve the governing differential equations.
130 citations
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TL;DR: In this article, a finite element model based on a higher-order shear deformation theory is developed to study the free vibration characteristics of laminated composite beams and the effects of in-plane inertia and rotary inertia are considered in the formulation of the mass matrix.
130 citations