scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented.
Abstract: In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton’s principle is presented, and a closed-form solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.

68 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigate the changes in the magnitude of natural frequencies and modal response introduced by the presence of a crack on an axially loaded uniform Timoshenko beam using a particular member theory.

68 citations

Journal ArticleDOI
TL;DR: In this paper, the static and dynamic responses of bi-directional functionally graded (BDFG) microbeams are investigated using von-Karman geometric nonlinearity and third-order shear deformation beam theory.

68 citations

Journal ArticleDOI
TL;DR: In this paper, the thermal buckling and postbuckling analysis of laminated composite beams with temperature-dependent material properties is presented, where the governing equations are based on first-order shear deformation beam theory (FSDT) and the geometrical nonlinearity is modeled using Green's strain tensor in conjunction with the von Karman assumptions.
Abstract: The thermal buckling and postbuckling analysis of laminated composite beams with temperature-dependent material properties is presented. The governing equations are based on the first-order shear deformation beam theory (FSDT) and the geometrical nonlinearity is modeled using Green's strain tensor in conjunction with the von Karman assumptions. The differential quadrature method (DQM) as an accurate, simple and computationally efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. A direct iterative method is employed to obtain the critical temperature (bifurcation point) as well as the nonlinear equilibrium path (the postbuckling behavior) of symmetrically laminated beams. The applicability, rapid rate of convergence and high accuracy of the method are established via different examples and by comparing the results with those of existing in literature. Then, the effects of temperature dependence of the material properties, boundary conditions, length-to-thickness ratios, number of layers and ply angle on the thermal buckling and postbuckling characteristic of symmetrically laminated beams are investigated.

68 citations

Journal ArticleDOI
TL;DR: In this paper, a non-classical beam model was developed to incorporate surface effects into the forced vibration analysis of nanobeams, and a cubic variation through the thickness of the nanobeam was considered for the normal stress component of the bulk to satisfy the surface equilibrium equations.

68 citations


Network Information
Related Topics (5)
Finite element method
178.6K papers, 3M citations
88% related
Fracture mechanics
58.3K papers, 1.3M citations
86% related
Numerical analysis
52.2K papers, 1.2M citations
84% related
Boundary value problem
145.3K papers, 2.7M citations
80% related
Stress (mechanics)
69.5K papers, 1.1M citations
78% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023194
2022437
2021509
2020487
2019540
2018508