Large Deflection Analysis of Non-Hinged Arch

2013 ◽  
Vol 705 ◽  
pp. 459-462
Author(s):  
Jia Wei Zhang ◽  
Sheng Wei Liu ◽  
He Min Liu ◽  
Ting Bin Liu ◽  
Jian Chang Zhao
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Finite Deformation ◽  
Theoretical Basis ◽  
Deformation Theory ◽  
Large Deflection ◽  
Nonlinear Differential Equations ◽  
Long Span ◽  
Deflection Analysis ◽  
Finite Deformation Theory

Based on the finite deformation theory nonlinear differential equations of uniform-sectional circular arch is deduced, and analytical solution for displacement of the non-hinged arch under load is obtained. This paper provides a theoretical basis for the analysis and calculation of the long span arch.

scholarly journals A Semi-Analytical Solution for Elastic Analysis of Rotating Thick Cylindrical Shells with Variable Thickness Using Disk Form Multilayers

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammad Zamani Nejad ◽  
Mehdi Jabbari ◽  
Mehdi Ghannad
Keyword(s):  
Cylindrical Shell ◽  
Analytical Solution ◽  
Differential Equations ◽  
Variable Thickness ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
First Order ◽  
Thick Cylinder ◽  
Good Agreement

Using disk form multilayers, a semi-analytical solution has been derived for determination of displacements and stresses in a rotating cylindrical shell with variable thickness under uniform pressure. The thick cylinder is divided into disk form layers form with their thickness corresponding to the thickness of the cylinder. Due to the existence of shear stress in the thick cylindrical shell with variable thickness, the equations governing disk layers are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations. Given that the cylinder is divided intondisks,nsets of differential equations are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. A numerical solution using finite element method (FEM) is also presented and good agreement was found.

scholarly journals A finite deformation theory of the urinary bladder.

1981 ◽  
Vol 135 (2) ◽  
pp. 149-154 ◽  
Author(s):  
HIROKI WATANABE ◽  
KIKUO AKIYAMA ◽  
TAKESI SAITO ◽  
FUMIYA OKI
Keyword(s):  
Urinary Bladder ◽  
Finite Deformation ◽  
Deformation Theory ◽  
Finite Deformation Theory

scholarly journals Effect of Material Nonlinearity on Large Deflection of Variable-Arc-Length Beams Subjected to Uniform Self-Weight

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Chainarong Athisakul ◽  
Boonchai Phungpaingam ◽  
Gissanachai Juntarakong ◽  
Somchai Chucheepsakul
Keyword(s):  
Differential Equations ◽  
Large Deflection ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Optimization Technique ◽  
Material Constant ◽  
Constitutive Law ◽  
Arc Length ◽  
Stress Strain Relation ◽  
Equilibrium Configurations

This paper presents a large deflection of variable-arc-length beams, which are made from nonlinear elastic materials, subjected to its uniform self-weight. The stress-strain relation of materials obeys the Ludwick constitutive law. The governing equations of this problem, which are the nonlinear differential equations, are derived by considering the equilibrium of a differential beam element and geometric relations of a beam segment. The model formulation presented herein can be applied to several types of nonlinear elastica problems. With presence of geometric and material nonlinearities, the system of nonlinear differential equations becomes complicated. Consequently, the numerical method plays an important role in finding solutions of the presented problem. In this study, the shooting optimization technique is employed to compute the numerical solutions. From the results, it is found that there is a critical self-weight of the beam for each value of a material constantn. Two possible equilibrium configurations (i.e., stable and unstable configurations) can be found when the uniform self-weight is less than its critical value. The relationship between the material constantnand the critical self-weight of the beam is also presented.

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