P.G. Glockner

Nonlinear analysis of multilayered shells

Abstract A large deformation theory for layered shells of arbitrarily varying thickness and using a piecewise smooth displacement field is developed. A system of layer coordinates is introduced which allows the results to be presented in a simple compact form analogous to the theory of monocoque shells.

Finite deformation and stability behaviour of spherical inflatables under axi-symmetric concentrated loads

Abstract The large deflection and stability behaviour of spherical inflatables subjected to a concentrated load applied at the apex and undergoing various degrees of wrinkling is analyzed. It is shown that for low profile inflatables, the behaviour of such structures under axi-symmetric concentrated loads is non-linear, without instability or limit point characteristics. On the other hand for high-profile membranes with height/span ratios greater than 0.5 and undergoing deflections equal to or greater than the initial height or radius of curvature of the structure, “snap through” behaviour is established. Ultimate loads for the totally wrinkled membranes are also established. The wrinkled region is considered in an Eulerian description satisfying equilibrium equations and the Gauss-Codazzi relations. The equations are solved numerically and the results are presented in non-dimensional form in a number of figures.

On the dynamic stability of viscoelastic perfect columns

Abstract The dynamic stability of simple supported perfect columns made of a linearly viscoelastic material and subjected to an axial compressive load, P, smaller than the classical Euler elastic buckling load, Pe, is examined. The solution to the integro-differential equation is obtained by means of Laplace transforms. In addition, an approximate solution is also derived by adopting the approximation technique introduced in [1]. The results are applied to a simple “three-element model” viscoelastic column.

The stability of viscoelastic perfect columns: A dynamic approach

Abstract In this article, the dynamic approach for stability analysis is used to obtain an approximate closed-form expression for the “viscoelastic critical load” of perfect columns made of a linear three-element model material. It is shown that a “critical time” for such structures cannot be defined independently of the type and nature of the disturbance causing instability in the sense of Lyapunov. Criteria are introduced to define a critical time that is independent of the magnitude of the disturbance. The nature of the disturbance, whether it is dynamic or static, however, still has a significant influence on the value of such a critical time.

On thermoelastic dielectrics

Abstract Constitutive equations for a linear thermoelastic dielectric are derived from the energy balance equation assuming dependence of the stored energy function on the strain tensor, the polarization vector, the polarization gradient tensor and entropy. A method is indicated for constructing a hierarchy of constitutive equations for materials with arbitrary symmetry by introducing various thermodynamic potentials. Maxwells relations are constructed for the thermodynamic potential W L . The entropy inequality is used to obtain stability conditions for an elastic dielectric in equilibrium under prescribed boundary constraints. Frequencies are explicitly determined for a plane wave propagating along the x 1 -axis in an infinite centro-symmetric isotropic thermoelastic dielectric.

On the thermodynamics of non-linear elastic dielectrics☆

A complete non-linear theory of thermoelastic dielectrics including polarization gradient effects is derived by using the two laws of thermodynamics and invariance requirements. Restrictions on the constitutive equations are obtained by using the classical form of the Clausius-Duhem inequality as well as a revised version used by Muller in which the entropy flux is not assumed, a priori, to be the ratio of heat flux to absolute temperature. Results from both formulations are compared.

On the statics of large-scale cylindrical floating membrane containers

Abstract Profiles of long cylindrical membranes to be used as large-scale floating containers are analyzed using membrane theory. A range of possible cross-sectional shapes for such containers are determined as functions of the relative density of the medium filling the container, the circumference of the container and a given volume efficiency defined in the paper. Characteristic features of such containers with the determined profiles are the relatively low membrane forces in the structure as well as the low level of internal over-pressure required to achieve such shapes. Consequently, a drastic reduction in requirements of stiffness and material strength is achieved. Such extremely light and hopefully inexpensive membrane structures could be utilized for the storing or transporting of large masses of “environmentally safe” liquids like, for example, fresh water.

Constitutive equations for elastic dielectrics

Abstract Assuming the free energy function to depend on the deformation gradient tensor, the polarization vector, the polarization gradient tensor and the temperature, material and spatial forms of the constitutive equations are obtained which involve the invariants constituting the minimal isotropy integrity basis for the free energy function. A special form of stored energy function, involving material descriptors, is used for anisotropic dielectrics. Upon suitable linearization. the results obtained here reduce to the constitutive equations for Voigts piezoelectricity theory and Mindlins theory for elastic dielectrics with polarization gradient.

Collapse by ponding of shells

Abstract The problem of stability of shells of positive Gaussian curvature subjected to a concentrated load, internal or external pressure and an accumulating ponding fluid in the depression caused by the load is the subject of this paper. Critical values of the load are calculated by a so called “geometrical method”, using variational Lagrangian principles. The shape of the shell is assumed to be nearly isometrical to the initial shape and its bending rigidity is taken into account. Simple relations for the critical load are obtained and the results presented in graphical form. The expressions and diagrams presented facilitate calculation of critical loads and describe the behaviour of the shell undergoing very large deflections.

Spherical inflatables under axisymmetric loads: another look∗☆

Abstract Further results on the axisymmetric large-deflection and stability behaviour of spherical pneumatics subjected to a vertical concentrated load applied at the apex are presented. In particular, the effect of the extensibility on the membranes behaviour is evaluated. For very high profiled structures, wrinkling at and next to the support is admitted, treating both the case in which a horizontal surface is present at the level of the supports as well as the “stove-pipe-like” support, in which the membrane deflects and wrinkles in a particular manner at the base above a certain load value. Finally, discontinuities in the load-deflection curves, resulting from insufficient accuracy in our earlier numerical work, are eliminated.