Multiply Loaded Timoshenko Beam on a Stressed Orthotropic Half-Plane via a Thin Elastic Layer

1993 ◽  
Vol 60 (2) ◽  
pp. 541-547 ◽  
Author(s):  
H. Bjarnehed
Keyword(s):  
Half Plane ◽  
Timoshenko Beam ◽  
Elastic Layer ◽  
Beam Theory ◽  
Singular Integral Equations ◽  
Uniaxial Stress ◽  
Shear Stresses ◽  
Fe Model ◽  
Tangential Load ◽  
Thin Elastic Layer

The problem of bonded contact between a uniform finite Timoshenko beam and an orthotropic half-plane via a thin elastic layer is considered in this paper. The beam is loaded by distributions of normal and tangential forces, and a uniaxial stress load is applied to the half-plane. The Timoshenko beam theory is extended in such a way that the tangential load is included when the shear contribution to the beam central line deflection is calculated. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated and numerically solved for the unknown interface stresses. A comparison with a corresponding FE-model is also performed.

Multiply Loaded Rigid Punch on a Stressed Orthotopic Half-Plane via a Thin Elastic Layer

1992 ◽  
Vol 59 (2S) ◽  
pp. S115-S122 ◽  
Author(s):  
Hans L. Bjarnehed
Keyword(s):  
Half Plane ◽  
Elastic Layer ◽  
Singular Integral Equations ◽  
Free Edge ◽  
Shear Stresses ◽  
Rigid Punch ◽  
Fem Model ◽  
Frictionless Contact ◽  
Thin Elastic Layer ◽  
Elastic Cushion

A uniaxially stressed orthotropic half-plane indented on the free edge by a multiply loaded rigid punch via a thin elastic layer is considered. The layer is formulated as a generalized Winkler cushion including also shear stresses and strains. Governing singular integral equations are stated for the unknown interface stresses between the cushion and the half-plane. Two kinds of friction conditions between the cushion and half-plane are treated, viz. completely adhesive and frictionless contact. An analytical solution for contact with a rigid cushion and a numerical solution with an elastic cushion are presented. Also, a comparison with a corresponding FEM model is performed. For frictionless contact, some analytical results concerning optimum design of the elastic cushion are given.

Exact Dynamic Analysis of Space Structures Using Timoshenko Beam Theory

AIAA Journal ◽  
2004 ◽  
Vol 42 (4) ◽  
pp. 833-839 ◽  
Author(s):  
Jen-Fang Yu ◽  
Hsin-Chung Lien ◽  
B. P. Wang
Keyword(s):  
Dynamic Analysis ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Space Structures

Optimal design of high-g MEMS piezoresistive accelerometer based on Timoshenko beam theory

2017 ◽  
Vol 24 (2) ◽  
pp. 855-867 ◽  
Author(s):  
Feng Liu ◽  
Shiqiao Gao ◽  
Shaohua Niu ◽  
Yan Zhang ◽  
Yanwei Guan ◽  
...  
Keyword(s):  
Optimal Design ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Timoshenko Beam Theory

Dominance of Shear Stresses in Early Stages of Impulsive Motion of Beams

1960 ◽  
Vol 27 (1) ◽  
pp. 132-138 ◽  
Author(s):  
H. H. Bleich ◽  
R. Shaw
Keyword(s):  
Differential Equations ◽  
Timoshenko Beam ◽  
Shear Stresses ◽  
Impulsive Motion ◽  
Early Stages ◽  
Plastic Analysis ◽  
Bending Stresses ◽  
Impulsive Forces

In order to compare the magnitude of bending stresses and shear stresses in beams under the action of impulsive forces, the values of these stresses are determined from the known differential equations for the Timoshenko beam. It is found that in the early stages, soon after the initiation of the motion, the shear stresses are of much larger magnitude than the bending stresses. This result indicates that for sufficiently large initial velocities first yielding will be in shear, a matter of consequence in plastic analysis.

scholarly journals Flexural Interpretation of Simply Supported Laminated Composite Beam

2020 ◽  
Vol 8 (5) ◽  
pp. 3559-3565
Keyword(s):  
Shear Deformation ◽  
Composite Beam ◽  
Laminated Composite ◽  
Beam Theory ◽  
Composite Beams ◽  
Shear Stresses ◽  
Bending Stress ◽  
Simply Supported ◽  
Laminated Composite Beam ◽  
Laminated Composite Beams

In this Paper, the analysis of simply supported laminated composite beam having uniformly distributed load is performed. The solutions obtained in the form of the displacements and stresses for different layered cross ply laminated composite simply supported beams subjected uniformly distributed to load. Different aspect ratio consider for different results in terms of displacement, bending stress and shear stresses. The shear stresses are calculated with the help of equilibrium equation and constitutive relationship. Using displacement field including trigonometric function of laminated composite beams are derived from virtual displacement principle. There are axial displacement, transverse displacement, bending stress and shear stresses. In addition, Euler-Bernoulli (ETB), First order shear deformation beam theory (FSDT), Higher order shear deformation beam theory (HSDT) and Hyperbolic shear deformation beam theory (HYSDT) solution have been made for comparison and better accuracy of solutions and results of static analyses of laminated composite beams for simply supported laminated composite beam.

Flexural Vibration Band Gap in a Periodic Fluid-Conveying Pipe System Based on the Timoshenko Beam Theory

2011 ◽  
Vol 133 (1) ◽  
Author(s):  
Dianlong Yu ◽  
Jihong Wen ◽  
Honggang Zhao ◽  
Yaozong Liu ◽  
Xisen Wen
Keyword(s):  
Finite Element Method ◽  
Band Gap ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Timoshenko Beam Theory ◽  
Flexural Wave ◽  
Vibration Band ◽  
Frequency Range ◽  
Pipe System

The flexural vibration band gap in a periodic fluid-conveying pipe system is studied based on the Timoshenko beam theory. The band structure of the flexural wave is calculated with a transfer matrix method to investigate the gap frequency range. The effects of the rotary inertia and shear deformation on the gap frequency range are considered. The frequency response of finite periodic pipe is calculated with a finite element method to validate the gap frequency ranges.

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