Optimum vibrating beams with stress and deflection constraints

The fundamental frequency of vibration of an Euler-Bernoulli or a Timoshenko beam of a specified constant volume is maximized subject to the constraint that under a prescribed loading the maximum stress or maximum deflection at any point along the beam axis will not exceed a specified value. In contrast with the inequality constraint which controls the minimum cross-section, the present inequality constraints lead to more meaningful designs. The inequality constraint on stresses is as easily implemented as the minimum cross-section constraint but the inequality constraint on deflection uses a treatment which is an extension of the matrix partitioning technique of prescribing displacements in finite element analysis

Some inconsistencies of the finite element method as applied to inelastic response

The inadequacy of a two noded beam-column element with a linear axial and a cubic transverse displacement field for inelastic analysis is demonstrated. For complete equilibrium satisfaction in the linear elastic range a three noded beam-column element is shown to be consistent. Next, the sensitivity of the inelastic response to numerical solutions of the inelastic response of a cantilever beam resulting from approximate integration of strain energy are brought out and finally, consequences of this on the nonlinear transient response of structures are considered

Nonlinear transient analysis via energy minimization

The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose

Efficiency of unconstrained minimization techniques in nonlinear analysis

Unconstrained minimization algorithms have been critically evaluated for their effectiveness in solving structural problems involving geometric and material nonlinearities. The algorithms have been categorized as being zeroth, first, or second order depending upon the highest derivative of the function required by the algorithm. The sensitivity of these algorithms to the accuracy of derivatives clearly suggests using analytically derived gradients instead of finite difference approximations. The use of analytic gradients results in better control of the number of minimizations required for convergence to the exact solution

Three dimensional inelastic finite element analysis of laminated composites

Formulations of the inelastic response of laminated composites to thermal and mechanical loading are used as the basis for development of the computer NALCOM (Nonlinear Analysis of Laminated Composites) computer program which uses a fully three dimensional isoparametric finite element with 24 nodes and 72 degrees of freedom. An incremental solution is performed with nonlinearities introduced as pseudoloads computed for initial strains. Equilibrium iteration may be performed at every step. Elastic and elastic-plastic response of boron/epoxy and graphite/epoxy graphite/epoxy and problems of curing 0/90 sub s Gr/Ep laminates with and without circular holes are analyzed. Mechanical loading of + or - 45sub s Gr/Ep laminates is modeled and symmetry conditions which exist in angle-ply laminates are discussed. Results are compared to experiments and other analytical models when possible. All models are seen to agree reasonably well with experimetnal results for off-axis tensile coupons. The laminate analyses show the three dimensional effects which are present near holes and free corners

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems

Study of improved modeling and solution procedures for nonlinear analysis

An evaluation of the ACTION computer code on an aircraft like structure is presented. This computer program proved adequate in predicting gross response parameters in structures which undergo severe localized cross sectional deformations

Enhancement of the Power Output of Photogalvanic Cells

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Study on Basic Mechanism of Reactive Armour

Two basic mechanisms which operate in the functioning of reactive armour are presented. Both the explosive effect and cutting of metal plates by a jet have been investigated. The angle of attack and the confinement of the explosive have been found most significant factors in reducing the penetrating power of the jet. The effect of detonating explosives has been investigated with radiography. Some of the significant effects, like detonation of explosive by the impact of the jet, expansion of covering plates, disturbance in coherence and reduction in the penetration of the jet have been observed. It is found that the jet penetration in a stack of mild steel plates is reduced to 30 per cent of its blank penetration in present set-ups. A theoretical model has been conceived to study the interaction of moving plates and the jet. The critical thickness and surface cut in plates have been calculated