Topic
Bending
About: Bending is a research topic. Over the lifetime, 41690 publications have been published within this topic receiving 427769 citations.
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TL;DR: In this article, a higher-order shear deformation theory for elastic shells was developed for shells laminated of orthotropic layers, which is a modification of the Sanders' theory and accounts for parabolic distribution of the transverse shear strains through thickness of the shell and tangential stress-free boundary conditions on the boundary surfaces.
1,009 citations
TL;DR: In this article, a 4-node plate bending element for linear elastic analysis is presented, as a special case, from a general nonlinear continuum mechanics based four-node shell element formulation.
Abstract: This communication discusses a 4-node plate bending element for linear elastic analysis which is obtained, as a special case, from a general nonlinear continuum mechanics based 4-node shell element formulation. The formulation of the plate element is presented and the results of various example solutions are given that yield insight into the predictive capability of the plate (and shell) element.
1,000 citations
Book•
01 May 1987
TL;DR: In this article, a major basic text on the theory and structural applications of laminated anisotropic plates is presented, with detailed coverage of problems of bending under transverse load, stability, and free-vibrations.
Abstract: A major basic text on the theory and structural applications of laminated anisotropic plates. Detailed coverage of problems of bending under transverse load, stability, and free-vibrations, as well as laminated beams, expansional strain effects, curved plates, and free-edge effects.
999 citations
TL;DR: In this paper, a microstructure-dependent Timoshenko beam model is developed using a variational formulation, which is based on a modified couple stress theory and Hamilton's principle.
Abstract: A microstructure-dependent Timoshenko beam model is developed using a variational formulation. It is based on a modified couple stress theory and Hamilton's principle. The new model contains a material length scale parameter and can capture the size effect, unlike the classical Timoshenko beam theory. Moreover, both bending and axial deformations are considered, and the Poisson effect is incorporated in the current model, which differ from existing Timoshenko beam models. The newly developed non-classical beam model recovers the classical Timoshenko beam model when the material length scale parameter and Poisson's ratio are both set to be zero. In addition, the current Timoshenko beam model reduces to a microstructure-dependent Bernoulli–Euler beam model when the normality assumption is reinstated, which also incorporates the Poisson effect and can be further reduced to the classical Bernoulli–Euler beam model. To illustrate the new Timoshenko beam model, the static bending and free vibration problems of a simply supported beam are solved by directly applying the formulas derived. The numerical results for the static bending problem reveal that both the deflection and rotation of the simply supported beam predicted by the new model are smaller than those predicted by the classical Timoshenko beam model. Also, the differences in both the deflection and rotation predicted by the two models are very large when the beam thickness is small, but they are diminishing with the increase of the beam thickness. Similar trends are observed for the free vibration problem, where it is shown that the natural frequency predicted by the new model is higher than that by the classical model, with the difference between them being significantly large only for very thin beams. These predicted trends of the size effect in beam bending at the micron scale agree with those observed experimentally. Finally, the Poisson effect on the beam deflection, rotation and natural frequency is found to be significant, which is especially true when the classical Timoshenko beam model is used. This indicates that the assumption of Poisson's effect being negligible, which is commonly used in existing beam theories, is inadequate and should be individually verified or simply abandoned in order to obtain more accurate and reliable results.
995 citations
TL;DR: In this paper, a modified couple stress theory was used for the bending of a Bernoulli-Euler beam and a variational formulation based on the principle of minimum total potential energy was employed.
Abstract: A new model for the bending of a Bernoulli–Euler beam is developed using a modified couple stress theory. A variational formulation based on the principle of minimum total potential energy is employed. The new model contains an internal material length scale parameter and can capture the size effect, unlike the classical Bernoulli–Euler beam model. The former reduces to the latter in the absence of the material length scale parameter. As a direct application of the new model, a cantilever beam problem is solved. It is found that the bending rigidity of the cantilever beam predicted by the newly developed model is larger than that predicted by the classical beam model. The difference between the deflections predicted by the two models is very significant when the beam thickness is small, but is diminishing with the increase of the beam thickness. A comparison shows that the predicted size effect agrees fairly well with that observed experimentally.
976 citations