An Analytical Model for Stress Analysis of a Tooth under the Orthodontic Force

2010 ◽  
Author(s):  
Yongxing Zhang ◽  
Lin Chen ◽  
Rui Li
Keyword(s):  
Stress Analysis ◽  
Analytical Model ◽  
Orthodontic Force

scholarly journals A closed-form solution for stress analysis of hollow circular cylinder structure under non-uniform external load and its engineering application

2020 ◽  
Vol 8 (1) ◽  
Author(s):  
Xiaoben Liu
Keyword(s):  
Circular Cylinder ◽  
Stress Analysis ◽  
Closed Form ◽  
Analytical Model ◽  
External Load ◽  
Closed Form Solution ◽  
Theory Of Elasticity ◽  
Engineering Practice ◽  
Principle Of Superposition ◽  
Hollow Circular Cylinder

Hollow circular cylinder structures are widely used in industry for their high bearing capacity. In some engineering cases, these structures are always subjected to complicated non-uniform external loads. For example, casings used for oil production are subjected to non-uniform ground stresses. In this study, a generalized closed-form analytical solution for stress analysis of hollow circular cylinder under non-uniform external load was derived. The common non-uniform external load was decomposed by Fourier series under the principle of superposition by theory of elasticity. Analytical solutions for stress results of sine or cosine series external load problems were obtained by the semi-inverse method. A baseline analysis of a casing under non-uniform ground stress was presented using the proposed analytical method and the finite element method to validate the accuracy of the proposed analytical model. A parametric analysis was conducted finally to discuss the effects of non-uniform coefficients on the stress results. Results show that, the hollow circular cylinder structure’s anti-collapse capacity will be strongly weakened, when the non-uniform coefficient increases. This proposed analytical model can be referenced in strength verification of hollow circular cylinder structures in engineering practice.

An Analytical Model for the Unbonded Flexible Pipe Stress Analysis With Consideration of Nonlinear Material Properties for Metal Layers

2010 ◽  
Author(s):  
Jian Liu ◽  
Zhimin Tan ◽  
Terry Sheldrake
Keyword(s):  
Stress Analysis ◽  
Analytical Model ◽  
Material Properties ◽  
Failure Modes ◽  
Nonlinear Material ◽  
Von Mises Stress ◽  
Stress And Strain ◽  
Flexible Pipe ◽  
Metal Layers ◽  
Plastic Stress

This paper presents an improved analytical model for the unbonded flexible pipe stress analysis with consideration of nonlinear material properties for metal layers. Analytical methods have often been used to analyse the stress and strain of flexible pipe systems because of their low cost and efficiency compared with detailed finite element modeling. Most of these kinds of models only consider the deformation of pipes within the elastic region. Such linear models can not be used directly to assess pipe failure modes such as the pipe burst strength, where the nonlinearity of the metallic material plays an important role in governing the pipe deformation and pipe structural capacity. The improved analytical model presented in this paper has fully considered the nonlinearity of metal layers such as the pressure armour and tensile armour layers because of their importance in resisting internal pressure and tension loads. Non-associative elasto-plastic stress strain curves obtained from experiments are used to simulate the metal layers. Von Mises stress is adopted in the model as the yield criterion of the metal layers. Radial return method (Simo and Taylor 1985 [1], Simo and Hughes 1998 [2]) is used to solve the plastic stress and strain of metal layers beyond the yield point. Due to its high nonlinearity from both system equations and material properties, Newton-Raphson method is adopted in the model as the solving method. The proposed study here considers tension, torque and pressure loads only for a straight pipe. The model predictions have been compared against measurements from Wellstream burst tests and failure tension tests performed over the full scale pipe samples. The prediction and experiment results agree.

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