Numerical calculation technique for large elastic-plastic transient deformations of thin shells.

AIAA Journal ◽  
1968 ◽  
Vol 6 (12) ◽  
pp. 2352-2359 ◽  
Author(s):  
JOHN W. LEECH ◽  
EMMETT A. WITMER ◽  
THEODORE H. H. PIAN
Keyword(s):  
Numerical Calculation ◽  
Thin Shells ◽  
Elastic Plastic ◽  
Calculation Technique

An Improved Numerical Calculation Technique for Large Elastic-Plastic Transient Deformations of Thin Shells: Part 2—Evaluation and Applications

1971 ◽  
Vol 38 (2) ◽  
pp. 429-436 ◽  
Author(s):  
L. Morino ◽  
J. W. Leech ◽  
E. A. Witmer
Keyword(s):  
Numerical Calculation ◽  
Computational Efficiency ◽  
Large Deformations ◽  
Thin Shells ◽  
Theoretical Formulation ◽  
Elastic Plastic ◽  
Calculation Technique ◽  
Good Agreement

Based upon the theoretical formulation presented in Part 1 of this paper, improvements in accuracy and computational efficiency are realized. Comparisons of predictions with experimental transient large deformations and strains show good agreement.

An Improved Numerical Calculation Technique for Large Elastic-Plastic Transient Deformations of Thin Shells: Part 1—Background and Theoretical Formulation

1971 ◽  
Vol 38 (2) ◽  
pp. 423-428 ◽  
Author(s):  
L. Morino ◽  
J. W. Leech ◽  
E. A. Witmer
Keyword(s):  
Numerical Calculation ◽  
Finite Difference ◽  
Arbitrary Shape ◽  
Large Deflection ◽  
Dynamic Responses ◽  
Thin Shells ◽  
Theoretical Formulation ◽  
Transient Loading ◽  
Elastic Plastic ◽  
Calculation Technique

Recent improvements are reported in both the theoretical formulation and in the finite-difference treatment of the relations governing the large-deflection elastic-plastic dynamic responses of thin shells of arbitrary shape to transient loading.

scholarly journals Calculation of thin isotropic shells beyond the elastic limit by the method of elastic solutions

2018 ◽  
Vol 196 ◽  
pp. 01014 ◽  
Author(s):  
Avgustina Astakhova
Keyword(s):  
Elastic Limit ◽  
Physical Nonlinearity ◽  
Elasticity Tensor ◽  
Thin Shells ◽  
Equilibrium Equations ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Internal Forces

The paper focuses on the model of calculation of thin isotropic shells beyond the elastic limit. The determination of the stress-strain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method. In the present work the building of the solution based on the equilibrium equations and geometric relations of linear theory of thin shells in curved coordinate system α and β, and the relations between deformations and forces based on the Hirchhoff-Lave hypothesis and the small elastic-plastic deformations theory are presented. Internal forces tensor is presented in the form of its expansion to the elasticity tensor and the additional terms tensor expressed the physical nonlinearity of the problem. The functions expressed the physical nonlinearity of the material are determined. The relations that allow to determine the range of elastic-plastic deformations on the surface of the present shell and their changing in shell thickness are presented. The examples of the calculation demonstrate the convergence of elastic-plastic deformations method and the range of elastic-plastic deformations in thickness in the spherical shell. Spherical shells with the angle of half-life regarding 90 degree vertical symmetry axis under the action of equally distributed ring loads are observed.

scholarly journals Plastic deformations in the ring spherical shells

2018 ◽  
Vol 251 ◽  
pp. 04060
Author(s):  
Avgustina Astakhova
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Thin Shells ◽  
Stress Dependence ◽  
Strain Intensity ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Linear Hardening ◽  
Elastic Plastic ◽  
Development Area

In the present work the results of the study of plastic deformations distribution in the thickness in ring spherical shells are presented. Resolving differential equations system is based on the Hirchhoff-Lave hypothesis, linear thin shells theory and small elastic-plastic deformations theory. The studying of the development area of plastic deformations in shells thickness are performed with using the results of the elastic solutions method. The basic relations of elastic solutions method that allow to determine the distribution areas of plastic deformations in shells thickness and along the generatrix are presented. The diagram of intense stress dependence from the strain intensity with linear hardening is received. The numerical solution is performed by orthogonal run method. Long and short spherical shells under the operation of three evenly distributed ring loads are observed. The shells have a tough jamming along the contour at the bottom and at the top. Dependency between tension intensity and deformations intensity is accepted for the case of a material linear hardening. Area of plastic deformations in shells thickness for three kinds of ring spherical shells are shown. The results for the loads differed by the value in twice are presented.

Elasto-Plastic Separation Frequency Analysis of Interference Fitted Joints in Lightweight Materials

2018 ◽  
Vol 15 (04) ◽  
pp. 1850026
Author(s):  
Volkan Kovan
Keyword(s):  
Plastic Deformation ◽  
Numerical Calculation ◽  
Numerical Analysis ◽  
Frequency Analysis ◽  
Automotive Industry ◽  
Calculation Methods ◽  
Interference Fit ◽  
Elastic Plastic ◽  
Steel Shaft ◽  
Thermal Interference

Aluminum has become a widely used material in the automotive industry due to the need for production of lighter automobiles. As the number and complexity of aluminum products increase, it becomes necessary to improve methods used to join these parts. Thermal interference fitting is one of these methods. It is not possible to calculate interference fit stresses accurately for all conditions using traditional calculation methods, and a method to calculate separation frequency of interference fitted aluminum parts is not available. This study investigates elastic–plastic interference fit stresses and separation frequencies of lightweight metal gear and steel shaft interference fitted joints (which have begun to be used widely in designs) using analytical and numerical calculation methods. It was found as a result of the study that plastic deformation occurred due to decreasing diameter, and increasing interference and numerical calculation methods produced accurate results. It was determined as a result of numerical analysis that the separation frequency of lightweight metal gears was lower in smaller interference fit diameters compared with steel gears, and that this increased in connection with increasing interference fit diameter and was found to be higher compared with steel gears.

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