SECOND-ORDER ELASITC ANALYSIS OF TWO-DIMENSIONAL FRAMES BASED ON TIMOSHENKO BEAM THEORY

2018 ◽  
Author(s):  
Yi-Qun Tang ◽  
◽  
Yao-Peng Liu ◽  
Keyword(s):  
Timoshenko Beam ◽  
Beam Theory ◽  
Second Order ◽  
Timoshenko Beam Theory ◽  
Two Dimensional

scholarly journals Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability

2020 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Exact Solution ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Second Order ◽  
Timoshenko Beam Theory ◽  
Bernoulli Beam ◽  
Closed Form Solutions ◽  
Order Analysis ◽  
Stiffness Matrices ◽  
Order Element

This paper presents an exact solution to the Timoshenko beam theory (TBT) for bending, second-order analysis, and stability. The TBT covers cases associated with small deflections based on shear deformation considerations, whereas the Euler–Bernoulli beam theory neglects shear deformations. A material law (a moment-shear force-curvature equation) combining bending and shear is presented, together with closed-form solutions based on this material law. A bending analysis of a Timoshenko beam was conducted, and buckling loads were determined on the basis of the bending shear factor. First-order element stiffness matrices were calculated. Finally second-order element stiffness matrices were deduced on the basis of the same principle.

scholarly journals Timoshenko Beam Theory Exact Solution For Bending, Second-Order Analysis, and Stability

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Exact Solution ◽  
Timoshenko Beam ◽  
Beam Theory ◽  
Second Order ◽  
Timoshenko Beam Theory ◽  
Bernoulli Beam ◽  
Closed Form Solutions ◽  
Order Analysis ◽  
Stiffness Matrices ◽  
Order Element

This paper presents an exact solution to the Timoshenko beam theory (TBT) for bending, second-order analysis, and stability. The TBT covers cases associated with small deflections based on shear deformation considerations, whereas the Euler–Bernoulli beam theory neglects shear deformations. A material law (a moment-shear force-curvature equation) combining bending and shear is presented, together with closed-form solutions based on this material law. A bending analysis of a Timoshenko beam was conducted, and buckling loads were determined on the basis of the bending shear factor. First-order element stiffness matrices were calculated. Finally second-order element stiffness matrices were deduced on the basis of the same principle.

On the Stresses and Deflections of Rectangular Beams

1956 ◽  
Vol 23 (3) ◽  
pp. 339-342
Author(s):  
B. A. Boley ◽  
I. S. Tolins
Keyword(s):  
Elasticity Theory ◽  
Infinite Series ◽  
Timoshenko Beam ◽  
Iterative Procedure ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Two Dimensional ◽  
Shear Forces ◽  
Strength Of Materials

Abstract The stresses and deflections in rectangular beams and bars are calculated from the two-dimensional elasticity theory by an iterative procedure previously derived. The loading consists of either normal or shear forces varying smoothly along the span. The results are obtained in the form of infinite series, whose first terms represent the elementary solutions of strength of materials; the accuracy of the Mc/I and P/A formulas can thus be estimated. A comparison with the Timoshenko beam theory is included.

scholarly journals Timoshenko Beam Theory: First-Order Analysis, Second-Order Analysis, Stability, and Vibration Analysis Using the Finite Difference Method

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Differential Equations ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Beam Theory ◽  
Second Order ◽  
Timoshenko Beam Theory ◽  
Governing Equations ◽  
Order Analysis ◽  
First Order ◽  
The Finite Difference Method

This paper presents an approach to the Timoshenko beam theory (TBT) using the finite difference method (FDM). The Timoshenko beam theory covers cases associated with small deflections based on shear deformation and rotary inertia considerations. The FDM is an approximate method for solving problems described with differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. In addition, the boundary conditions and not the governing equations are applied at the beam’s ends. The model developed in this paper consisted of formulating differential equations with finite differences and introducing additional points at the beam’s ends and at positions of discontinuity (concentrated loads or moments, supports, hinges, springs, brutal change of stiffness, spring-mass system, etc.). The introduction of additional points allowed us to apply the governing equations at the beam’s ends. Moreover, grid points with variable spacing were considered, the grid being uniform within beam segments. First-order, second-order, and vibration analyses of structures were conducted with this model. Furthermore, tapered beams were analyzed (element stiffness matrix, second-order analysis, vibration analysis). Finally, a direct time integration method (DTIM) was presented; the FDM-based DTIM enabled the analysis of forced vibration of structures, with damping taken into account. The results obtained in this paper showed good agreement with those of other studies, and the accuracy was increased through a grid refinement. Especially in the first-order analysis of uniform beams, the results were exact for uniformly distributed and concentrated loads regardless of the grid.

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
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