Abstract
A theoretical approach was developed for predicting the plastic deformation of a cylindrical shell subject to asymmetric dynamic loads. The plastic deformation of the leading generator of the shell is found by solving for the transverse deflections of a rigid-plastic beam/string-on-foundation. The axial bending moment and tensile force in the beam/string are equivalent to the longitudinal bending moments and membrane forces of the shell, while the plastic foundation force is equivalent to the shell circumferential bending moment and membrane resistances. Closed-form solutions for the transient and final deformation profile of an impulsive loaded shell when it is in a “string” state were derived using the eigenfunction expansion method. These results were compared to DYNA 3D predictions. The analytical predictions of the transient shell and final centerline deflections were within 25% of the DYNA 3D results.
Highlights
The objective of this study is to develop a general approach for predicting the plastic deformation of a cylindrical shell subject to dynamic loading
Calculations show that, for the given diameter to thickness ratio of the shells considered by DYNA 3D, the equivalent ring crushing resistance, i.e., the equivalent plastic foundation force, in a bending mode is 2 orders of magnitude less than that in a membrane mode
An equivalent ring crushing resistance that assumes both membrane and bending modes would be lower than one calculated with only a membrane mode. This explains why analytical predictions were less than the numerical solutions
Summary
A theoretical approach was developed for predicting the plastic deformation of a cylindrical shell subject to asymmetric dynamic loads. The plastic deformation of the leading generator of the shell is found by solving for the transverse deflections of a rigid-plastic beam/string-on-foundation. The axial bending moment and tensile force in the beam/string are equivalent to the longitudinal bending moments and membrane forces ofthe shell, while the plastic foundation force is equivalent to the shell circumferential bending moment and membrane resistances. Closed-form solutions for the transient and final deformation profile of an impulsive loaded shell when it is in a "string" state were derived using the eigenfunction expansion method. These results were compared to D YNA 3D predictions. The analytical predictions of the transient shell and final centerline deflections were within 25% of the DYNA 3D results
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