Flexible Shallow Shells Research Articles

Nonlinear Modes of Motion of Thin Circular Cylindrical Shells

Free flexural vibrations of a simply supported shell are studied within the framework of the nonlinear theory of flexible shallow shells. It is assumed that large‐amplitude flexural vibrations are coupled with radial vibrations of the shell. Modal equations are derived by the Bubnov–Galerkin method. Periodic solutions are obtained by the Krylov–Bogolyubov method. The skeleton curve of the soft type obtained using a nonlinear finite‐dimensional shell model agrees with available experimental data.

Solution of two-dimensional problems of the statics of flexible shallow shells by spline approximation

Spline functions have come into increasingly wide use recently in the solution of boundary-value problems of the theory of elasticity of plates and shells. This development stems from the advantages offered by spline approximations compared to other methods. Among the most important advantages are the following: (1) the behavior of the spline in the neighborhood of a point has no effect on the behavior of the spline as a whole; (2) spline interpolation converges well compared to polynomial interpolation; (3) algorithms for spline construction are simple and convenient to use. The use of spline functions to solve linear two-dimensional problems on the stress-strain state of shallow shells and plates that are rectangular in plan has proven their efficiency and made it possible to expand the range of problems that can be solved. The approach proposed in these investigations is based on reducing a linear two-dimensional problem to a unidimensional problem by the spline unidimensional problem by the method of discrete orthogonalization in the other coordinate direction. Such an approach makes it possible to account for local and edge effects in the stress state of plates and shells and obtain reliable solutions with complex boundary conditions. In the present study, wemore » take the above approach, employing spline functions to solve linear problems, and use it to also solve geometrically nonlinear problems of the statics of shallow shells and plates with variable parameters.« less

Analysis of inhomogeneous flexible shallow shells with mixed boundary conditions

Analysis of inhomogeneous flexible shallow shells with mixed boundary conditions

A modified approach to large deflection analyses of thin elastic plates under thermal loading

The coupled system of three partial differential equations governing a flexible shallow shell dynamics is analysed. No any prior assumptions about the temperature distribution through the shell thickness are applied. The efficiency of the method used here when applied to the solution of integral–differential equations with different dimensions (three-dimensional equations related to the Kirchhoff–Love model) and of different type (heat transfer equations and the hyperbolic equations of shell theory) is demonstrated. Many computational results are reported and discussed.

Elastic-plastic deformation of a flexible shallow shell with a circular hole

Elastic-plastic deformation of a flexible shallow shell with a circular hole

Motion of a Flexible Shallow Spherical Shell in Orbit

A mathematical model for the motion of a large, flexible shallow spherical shell in a circular orbit is presented. For small elastic displacements and attitude angles the linearized equations for the roll and yaw (out-of-plane) motions completely separate from the pitch (in-plane) and elastic motions. However, the pitch and only the axisymmetric elastic modes are seen to be coupled in the linear range. With the shell's symmetry axis following the local vertical, the structure undergoes a static deformation under the influence of gravity and inertia. Further, the pitch and roll motions are unstable due to the unfavorable moment of inertia distribution. A rigid dumbbell connected to the shell at its apex by a spring-loaded double-gimball joint is proposed to stabilize the structure gravitationally. A sensitivity study of the system response characteristics to the key system parameters is carried out.

Variational principles of the theory of elastic flexible shallow shells

Variational principles of the theory of elastic flexible shallow shells

Dynamics problems for elastic-plastic flexible shallow shells

Dynamics problems for elastic-plastic flexible shallow shells

Elastoplastic deformations of flexible ribbed shallow shells

Elastoplastic deformations of flexible ribbed shallow shells

Calculations of a flexible shallow shell of elliptic form

Calculations of a flexible shallow shell of elliptic form

Viscoelastic behavior of flexible shallow shells

Viscoelastic behavior of flexible shallow shells

Critical states of flexible orthotropic shallow shells

Critical states of flexible orthotropic shallow shells

Stability of orthotropic viscoelastic shells

Abstract : The authors review the basic principles of the closed quasilinear quadratic theory of viscoelasticity of physically nonlinear media as proposed by A. A. Il'yushin and P. M. Ogibalov. A system of nonlinear equations of bending and stability is proposed for flexible (i.e. with regard to geometric nonlinearity) shallow plates and shells made from orthotropic materials with linear properties (fiberglass-reinforced plastics). It is assumed that the hypothesis of straight normals is applicable to these plates and shells. It is also assumed that stresses normal to the middle surface are insignificantly small compared to the other components and that the shells and plates remain orthotropic throughout the entire deformation process. A method of solving the proposed equations is outlined and illustrated by analysis of the stability of a rectangular orthotropic plate of slightly curved panel of fiberglass-reinforced plastic with given stress relaxation curves. The results agree satisfactorily with experimental data on creep in a square plate hinged at the edges. Methods are also given for determining the upper and lower critical loads as related to the loading conditions and the critical time. A viscoelastic solution is found by the proposed method for the problem of stability of a compressed cylindrical shell and compared with an elastic solution found by the Ritz method.

The solution of a problem concerning the flexure of a flexible shallow shell

The solution of a problem concerning the flexure of a flexible shallow shell

Analysis of flexible plates and shallow shells by the method of V. Z. Vlasov

Analysis of flexible plates and shallow shells by the method of V. Z. Vlasov