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Viscoplastic axisymmetrical buckling of spherical shell impulse subjected to radial pressure
Abstract The solution of viscoplastic axisymmetrical buckling of a complete thin spherical shell subjected to radial pressure impulse is presented. Analytically, the problem is formulated as a superposition of small perturbations on the basic unperturbed motion. The amplitudes of perturbed motion are restricted to be so small that the homogeneous compressive deformation predominates over the local bending. This condition allows the constitutive equations to be linearized by the expansion into Taylor's series in the vicinity of unperturbed motion. As a result, a set of two linear partial differential equations of the fifth order is obtained for describing the perturbed motion of the shell. The functional coefficients of these equations are determined by the solution for the unperturbed motion. The governing set of equations is solved using the series of Legendre's functions. As a result, for the time-dependent amplitudes in the series, the set of two ordinary equations with variable coefficients is arrived at. It turns out that certain harmonics grow very rapidly and cause the shell to exhibit a characteristic wrinkled shape which is characterized by a critical mode number. This property of the amplitudes is used to determine the threshold impulse that a shell can tolerate without excessive deformation. The influence of the meridional displacement on the magnitude of radial displacement, buckling mode and critical impulse is investigated. Also, the influence of the viscosity and the initial imperfections of the geometry and loading is shown. The numerical results for a steel shell are presented diagrammatically.
Viscoplastic axisymmetrical buckling of spherical shell impulse subjected to radial pressure
Abstract The solution of viscoplastic axisymmetrical buckling of a complete thin spherical shell subjected to radial pressure impulse is presented. Analytically, the problem is formulated as a superposition of small perturbations on the basic unperturbed motion. The amplitudes of perturbed motion are restricted to be so small that the homogeneous compressive deformation predominates over the local bending. This condition allows the constitutive equations to be linearized by the expansion into Taylor's series in the vicinity of unperturbed motion. As a result, a set of two linear partial differential equations of the fifth order is obtained for describing the perturbed motion of the shell. The functional coefficients of these equations are determined by the solution for the unperturbed motion. The governing set of equations is solved using the series of Legendre's functions. As a result, for the time-dependent amplitudes in the series, the set of two ordinary equations with variable coefficients is arrived at. It turns out that certain harmonics grow very rapidly and cause the shell to exhibit a characteristic wrinkled shape which is characterized by a critical mode number. This property of the amplitudes is used to determine the threshold impulse that a shell can tolerate without excessive deformation. The influence of the meridional displacement on the magnitude of radial displacement, buckling mode and critical impulse is investigated. Also, the influence of the viscosity and the initial imperfections of the geometry and loading is shown. The numerical results for a steel shell are presented diagrammatically.
Viscoplastic axisymmetrical buckling of spherical shell impulse subjected to radial pressure
Wojewódzki, W. (author) / Lewiński, P. (author)
Engineering Structures ; 3 ; 168-174
1981-01-01
7 pages
Article (Journal)
Electronic Resource
English
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