An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

Aeroelastic analysis of an idealized landing gear door in subsonic potential flow

Landing gear doors on aircraft have experienced flutter during preliminary flight testing. While designs vary widely, landing gear doors are typically plate-like structures with a relatively rigid actuator attached to their inside surface. To better understand the aeroelasticity of landing gear doors, this study investigates the aeroelastic stability of an idealized model. The model consists of a hinged plate with an interior constraint approximating the actuator attachment. The plate is subject to uniform flow, and an unsteady vortex lattice model is coupled to the structural model to predict critical flow velocities. The location and footprint area of the internal constraint, along with plate aspect and mass ratios, are varied to investigate a large parameter space. Results reveal that the critical flow speed and instability mechanism are sensitive to the postulated actuator placement. In general, flutter is the dominant mode of instability when the actuator is postulated in the leading quarter of the plate. In other postulated locations, divergence dominates. However, the exact shape and location of the boundary between flutter and divergence is configuration dependent and found to be especially sensitive to changes in aspect ratio.     

Limit states of elastic–viscoplastic plate deformations caused by repeated shock wave-loadings. Part 1: Experimental observation

In the present work, the evolution of the inelastic centre deflections of shock wave-loaded circular metal plates due to repeated loadings is studied experimentally and numerically. These displacements are compared to those of quasi-statically deformed plates loaded by a pressure equal to the peak pressure of the impulsive loading. Thereby three types of permanent centre deflections are observed: (1) The quasi-statically obtained deflection is exceeded by the middle point displacement of a dynamically loaded structure already after the first impulse and tends towards a limit state after repeated shock wave-loadings. (2) The centre deflection of the impulsively loaded plate exceeds also the quasi-statically caused deflection and does not increase after repeated impulsive loadings any more. (3) The permanent middle point displacement of a dynamically loaded plate is smaller than the deflection of a quasi-statically loaded one and tends towards the middle point displacement of the quasi-static counterpart after repeated shock wave loadings. This phenomenon is known in the literature as ‘Pseudo-shakedown’.

In Part 1 of this study the experimental observation is described, followed by a theoretical study in Part 2.     

Modified Kirchhoff's theory of plates including transverse shear deformations

A primary flexure problem defined by Kirchhoff theory of plates in bending is considered. Significance of auxiliary function introduced earlier in the in-plane displacements in resolving Poisson-Kirchhoff's boundary conditions paradox is reexamined with reference to reported sixth order shear deformation theories, in particular, Reissner's theory and Hencky's theory. Sixth order modified Kirchhoff's theory is extended here to include shear deformations in the analysis.     

Effect of air gaps on ballistic resistance of targets for conical impactors

High velocity penetration of a rigid conical impactor into a ductile target with air gaps between the plates is studied using the cylindrical cavity expansion approximation describing impactor–target interaction. It is showed that the latter model predicts improvement of the ballistic performance of the target with the increase of air gaps. It is found analytically that the ballistic limit velocity of the target consisting of N plates with a fixed total thickness with large air gaps increases with the increase of N. The conditions are discussed when the predicted effects can be most pronounced.     

Abnormal long wave dispersion phenomena in a slightly compressible elastic plate with non-classical boundary conditions

A two parameter asymptotic analysis is employed to investigate some unusual long wave dispersion phenomena in respect of symmetric motion in a nearly incompressible elastic plate. The plate is not subject to the usual classical traction free boundary conditions, but rather has its faces fixed, precluding any displacement on the boundary. The abnormal long wave behaviour results in the derivation of non-local approximations for symmetric motion, giving frequency as a function of wave number. Motivated by these approximations, the asymptotic forms of displacement components established and long wave asymptotic integration is carried out.     

Complex potential formalisms for bending of inhomogeneous monoclinic plates including transverse shear deformation

This paper develops complex potential formalisms for the solution of the bending problem of inhomogenoeus anisotropic plates, on the basis of the most commonly used refined plate theories. Being an initial step in that direction, it works out such formalisms only in connection with the bending problem of shear deformable homogeneous plates as well as plates having a special type of inhomogeneity along their thickness direction. The adopted type of inhomogeneity is however still general enough to include certain classes of plates made of functionally graded material as well as the classes of cross- and angle-ply symmetric laminates as particular cases. The basic formalism, similar to that developed by Stroh in plane strain elasticity, is detailed in relation with the equilibrium equations of a generalized plate theory that accounts for the effects of transverse shear deformation and includes conventional, refined theories as particular cases. Some interesting specializations, related to the most important of those conventional plate theories, are then presented and discussed separately. Hence, the outlined formalisms provide, for the first time in analytical form, the general solution of the partial differential equations associated with the most commonly used refined, elastic plate theories.     

Vibration of an elastic plate under action of an incompressible fluid in case of N = 0 approximation of I. Vekua's hierarchical models

This article deals with the study of the interaction between an elastic plate with constant thickness and an incompressible fluid when the plate is approximated by the N?=?0 order term of Vekua's hierarchical model.     

Plastic Plate Bending Problem with Friction on the Boundary and Uncertain Input Data

A thin plate made of a plastic material obeying the Hencky–Mises stress-strain law is considered. On a part of the boundary displacements and/or rotations with friction are prescribed. The model leads to a variational inequality of the second kind with a nonlinear monotone operator. Since the material function, loading, and friction coefficients are uncertain, we employ the worst scenario method. The existence of a worst scenario and a convergence of approximate solutions is proved.     

Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates

Some models for axially moving orthotropic thin plates are investigated analytically via methods of complex analysis to derive estimates for critical plate velocities. The linearized Kirchhoff plate theory is used, and the energy forms of steady-state models are considered with homogeneous and inhomogeneous tension profiles in the cross direction of the plate. With the help of the energy forms, some limits for the divergence velocity of the plate are found analytically. In numerical examples, the derived lower limits for the divergence velocity are analyzed for plates with small flexural rigidity.