Stability and Vibrations of Geometrically Nonlinear Cylindrioally Orthotropic Circular Plates

Introduction Axisymmetrical deformations of geometrically nonlinear cylindrically orthotropic circular plates under a multiparametric system of loading where thermal stresses are also taken into account are investigated. In theses cases there may be nonuniqueness of equilibrium states, i.e., for the same parameter of loading or temperature, there can exist a number of equilibrium states for the plate. This effect may lead to a loss of stability by snapping of different kinds. Therefore, there is a necessity to study the stability of all the possible equilibrium states. The numerical method used for investigating the stability of the equilibrium states is the well-known dynamical method (method of small vibrations). To the best of our knowledge, this method was used for the first time for nonlinear shells in [1] and systematically for isotropic geometrically nonlinear plates and shells in Since eigenfrequencies (eigenvalues) are the basis for this method (when the eigenfrequencies are real the examined equilibrium states are stable in the corresponding sense, and when they are imaginary these states are unstable) it is necessary to find them for plates under different conditions. As opposed to the linear case the eignfrequencies in question are dependent on the values and character of the external cross forces and temperature

Modeling the elastic deformation of polymer crusts formed by sessile droplet evaporation

Evaporating droplets of polymer or colloid solution may produce a glassy crust at the liquid-vapour interface, which subsequently deforms as an elastic shell. For sessile droplets, the known radial outward flow of solvent is expected to generate crusts that are thicker near the pinned contact line than the apex. Here we investigate, by non-linear quasi-static simulation and scaling analysis, the deformation mode and stability properties of elastic caps with a non-uniform thickness profile. By suitably scaling the mean thickness and the contact angle between crust and substrate, we find data collapse onto a master curve for both buckling pressure and deformation mode, thus allowing us to predict when the deformed shape is a dimple, mexican hat, and so on. This master curve is parameterised by a dimensionless measure of the non-uniformity of the shell. We also speculate on how overlapping timescales for gelation and deformation may alter our findings.Comment: 8 pages, 7 figs. Some extra clarification of a few points, and minor corrections. To appear in Phys. Rev.

Volume-controlled buckling of thin elastic shells: Application to crusts formed on evaporating partially-wetted droplets

Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and the substrate. This volume constraint mimics the incompressibility of the unevaporated solvent. Discontinuous buckling is found to occur for sufficiently thin and/or large contact angle shells, and robustly takes the form of a single circular region near the boundary that `snaps' to an inverted shape, in contrast to externally pressurised shells. Scaling theory for shallow shells is shown to well approximate the critical buckling volume, the subsequent enlargement of the inverted region and the contact line force.Comment: 7 pages in J. Phys. Cond. Mat. spec; 4 figs (2 low-quality to reach LANL's over-restrictive size limits; ask for high-detailed versions if required

On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities

Weakly clamped uniformly stretched thin elastic plates can experience edge buckling when subjected to a transverse pressure. This situation is revisited here for a circular plate, under the assumption of finite rotations and negligible bending stiffness in the pre-buckling range. The eigenproblem describing this instability is formulated in terms of two singularly perturbed fourth-order differential equations involving the non-dimensional bending stiffness ε>0. By using an extension of the asymptotic reduction technique proposed by Coman and Haughton (Acta Mech 55:179–200, 2006), these equations are formally reduced to a simple second-order ordinary differential equation in the limit ε→0+. It is further shown that the predictions of this reduced problem are in excellent agreement with the direct numerical simulations of the original bifurcation equations

Damping

Aerospace Engineerin

Energy-based mechanical model for mixed mode failure of laminated composites

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76674/1/AIAA-12639-806.pd