On the dynamic behaviour of the Timoshenko beam finite elements
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TLDR
In this paper, various finite element models of the Timoshenko beam theory for static analysis are reviewed, and a novel derivation of the 4 × 4 stiffness matrix (for the pure bending case) of the superconvergent finite element model for static problems is presented using two alternative approaches: (1) an assumed-strain finite-element model of the conventional Timoshenkobeam theory, and (2) assumed-displacement finite elements model of a modified Timoshenko-beam theory.Abstract:
First, various finite element models of the Timoshenko beam theory for static analysis are reviewed, and a novel derivation of the 4 × 4 stiffness matrix (for the pure bending case) of the superconvergent finite element model for static problems is presented using two alternative approaches: (1) assumed-strain finite element model of the conventional Timoshenko beam theory, and (2) assumed-displacement finite element model of a modified Timoshenko beam theory. Next, dynamic versions of various finite element models are discussed. Numerical results for natural frequencies of simply supported beams are presented to evaluate various Timoshenko beam finite elements. It is found that the reduced integration element predicts the natural frequencies accurately, provided a sufficient number of elements is used.read more
Citations
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Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories
TL;DR: In this article, the fundamental frequency analysis of functionally graded (FG) beams having different boundary conditions is analyzed within the framework of the classical, the first-order and different higher-order shear deformation beam theories.
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Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature
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Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh–Ritz method
TL;DR: In this paper, the free vibration analysis of functionally graded material (FGM) beams subjected to different sets of boundary conditions is performed based on the classical and first order shear deformation beam theories.
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Free vibration analysis of Timoshenko beams by DSC method
Ömer Civalek,Okyay Kiracioglu +1 more
TL;DR: In this paper, Discrete singular convolution method is used for numerical solution of equation of motion of Timoshenko beam, which is very effective for the study of vibration problems of timoshenko beam.
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A generalized bond-based peridynamic model for quasi-brittle materials enriched with bond tension-rotation-shear coupling effects
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TL;DR: In this paper, a generalized bond-based micropolar peridynamic model is proposed to simulate the nonlinear deformation and mixed-mode crack propagation of quasi-brittle materials under arbitrary dynamic loads.
References
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Book
An Introduction to the Finite Element Method
TL;DR: Second-order Differential Equations in One Dimension: Finite Element Models (FEM) as discussed by the authors is a generalization of the second-order differential equation in two dimensions.
Theory and analysis of elastic plates
TL;DR: The theory and analysis of Euler-Bernoulli Beams and Timoshenko Beams is discussed in this article. But the analysis of the classical plate theory is not considered.
Book
Variational Methods in Theoretical Mechanics
J. Tinsley Oden,J. N. Reddy +1 more
TL;DR: The role of Variational Theory in Mechanics is discussed in this article, where Galerkin's method is used to approximate the distance of a nonlinear operator from a given point of view.
Journal ArticleDOI
On locking-free shear deformable beam finite elements
TL;DR: In this article, a locking-free finite element model using the form of the exact solution of the Timoshenko beam theory is developed, which yields exact nodal values for the generalized displacements for constant material and geometric properties of beams.