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.

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.

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

Theoretical and Experimental Studies of Transient Elastic-Plastic Large Deflections of Geometrically Stiffened Rings

1975 ◽  
Vol 42 (4) ◽  
pp. 793-799
Author(s):  
R. W. H. Wu ◽  
E. A. Witmer
Keyword(s):  
Large Deflection ◽  
Permanent Deformation ◽  
Experimental Studies ◽  
Dynamic Responses ◽  
Elastic Plastic ◽  
Transient Strain ◽  
Theoretical Predictions ◽  
Structural Responses ◽  
Circular Rings ◽  
Freely Suspended

Finite-element formulations have been derived for the large-deflection elastic-plastic dynamic responses of arbitrarily curved two-dimensional beam structures which may consist of hard-boned, multilayer, geometrically stiffened configurations. Experiments have been conducted for structural responses of geometrically stiffened, freely suspended, circular rings of 6061-T6511 aluminum alloy to intense explosive loading which induces large-deflection elastic-plastic transient and permanent deformations of the structure. Very good correlation of the measured permanent deformation and transient strain with theoretical predictions is demonstrated.

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.

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