Presence Of Initial Stresses Research Articles

Quasi-P and quasi-S waves in a self–reinforced medium under initial stresses and under gravity

The present paper is concerned with the propagation of plane waves in self–reinforced media. The velocities of quasi-P and quasi-S waves in an unbounded self–reinforced medium under initial stresses and under gravity field have been derived. Also the reflection coefficients and the partition of energy of reflected quasi-P and quasi-SV waves due to incident quasi-P and quasi-SV waves have been obtained under the influence of initial stress and gravity field. It has been noticed that the velocities, reflection coefficients and energy coefficients not only depend on the initial stress and gravity but also on the direction of propagation. The results are in agreement with the classical case in the absence of initial stresses and gravity. In presence of initial stresses and gravity field, the velocities, reflection coefficients and energy coefficients of quasi-P and quasi-S waves are calculated numerically and are presented by means of graphs.

Elastic instability and free vibration analyses of tapered thin-walled beams by the power series method

In this paper, the flexural-torsional buckling and free vibration of tapered thin-walled beam-columns with arbitrary cross-section shape are extensively investigated. The governing equilibrium equations and motion equations are obtained from the stationary condition of the potential energy. The strain energy is derived in presence of initial stresses. In the work of the applied forces, effects of load eccentricities from shear and centroid centerlines are taken into account. Free vibration is considered in presence of harmonic excitations. In presence of arbitrary boundary conditions and variable cross-section properties, a semi-analytical approach based on power series method is adopted in solution. According to this method, displacements and geometric constants are approximated by polynomial functions up to a certain order, where accurate results are reached. The flexural-torsional buckling loads or natural frequencies are determined by solving an eigenvalue problem. In order to measure the accuracy and to check the validity of the present method, several examples including flexural-torsional behavior and free vibration analysis of non-prismatic thin-walled members with web and flange tapering and various boundary conditions are considered. The obtained results are compared to the finite element simulations and other available solutions.

Analysis of fiber reinforced composite plates subjected to transverse impact in the presence of initial stresses

The paper discusses the response of a large uniaxially reinforced graphite/epoxy composite plate with tensile pre-stresses in its plane when it is subjected to transverse impact loading. Sveklo’s contact theory for orthotropic materials has been used to describe the interaction between the plate and the impactor. Both uniaxial and biaxial tensile pre-stresses have been considered and their effects on the contact force, contact duration and the central deflection of the plate have been evaluated. Whereas the effect on the contact force is marginal, the central deflection and the contact duration are influenced significantly by the pre-stresses. The pre-stress transverse to the direction of fibers plays a greater role vis-à-vis the pre-stress parallel to the fibers.

PIEZOELECTRIC ACTUATOR AND SENSOR MODELS FOR AN INFLATED TOROIDAL SHELL

Due to their low mass and conformability, actuators and sensors made of active materials can be used in the vibration control of inflatable structures. In this study, we model piezoelectric patches attached to an inflated toroidal shell as actuators and sensors. Using Sanders' shell theory in the presence of initial stresses, the generalised forces due to the piezoelectric actuators are derived for the inflated toroidal shell assuming quasi-static conditions. The derivations are given for both unimorph and bimorph configurations. Effects of the mass and stiffness of the patches are incorporated in the equations of motion. Thereafter, a sensor equation is presented. Within linear shell theory, the methodology is quite general in nature and can be applied easily to other types of shells and membranes. To demonstrate this, we specialise the actuator and sensor equations for a circular cylinder. Using the formulations for the inflated toroidal shell, the modal forces and modal sensing constants are calculated for different sizes and locations of the piezoelectric patches. Along with this, controllability and observability indices are calculated to quantify the performance of the actuators and sensors. A study of the stiffness and mass effects of the piezoelectric patches is performed using frequency response function.

VIBRATION OF INITIALLY STRESSED REDDY PLATES ON A WINKLER–PASTERNAK FOUNDATION

Treated herein is the vibration of isotropic Reddy plates. The plates considered are of general polygonal shape and their edges are all simply supported. Complicating effects such as the presence of initial stresses and a Winkler–Pasternak foundation are also considered. It is shown herein that the vibration solution can be readily obtained from the classical Kirchhoff plate vibration results because of the mathematical similarity of the two kinds of problems. The mathematical analogy permits the development of an exact relationship that links the natural frequencies of the initially stressed Reddy plates resting on a Winkler–Pasternak foundation to the corresponding classical Kirchhoff plate solutions without the presence of complicating effects.

Optimum design of stiffened structures with constraint on the frequency in the presence of initial stresses

Structural optimization often leads to simultaneity of two or more failure modes. The interaction between failure modes must be included in the constraint set for a safe design. In this paper, stiffened cylindrical panels and waffle plates are designed with constraints on static instabilities, natural frequencies and initially stressed vibration frequencies. The interaction between instability and the natural frequency of the structure is considered. The erosion of structural safety when instability and free vibrations are assumed to be independent of each other is shown. Numerical examples are included to illustrate the interaction phenomenon.

Optimum design of stiffened cylindrical panels with constraint on the frequency in the presence of initial stresses

AbstractThis paper presents the optimum design of stiffened cylindrical panels with weight as the objective function and constraints on the frequencies in the presence of initial stresses, using unconstrained minimization techniques of non‐linear mathematical programming problem. The interaction between the buckling constraints and the frequency constraints in the presence of initial stresses are included in the formulation. Loss of load carrying capacity due to imperfection and due to suddenly applied loads are included in the buckling analyses. Results for cylindrical shell are obtained by setting the panel angle to 360 degrees. The relationship between the weight of the cylinder and the panel (a segment of the cylinder) is examined.

Buckling of a long cylindrical shell containing an elastic core

A long, thin, circular cylindrical shell containing an elastic core, bonded to the inner surface of the shell, is subjected to a uniform external hydrostatic pressure. Stability of equilibrium of the shell is investigated by considering possible neighboring equilibrium states. The loading exerted by the elastic core on the shell in the deformed state is found by solving an associated boundary value problem of the linearized theory of elasticity in the presence of initial stresses. An expression for the buckling pressure of the shell is derived, and results are presented for a wide range of shell and medium parameters.