Dynamic response of a beam on elastic foundation of finite depth under a moving force

In this paper, dynamic response of an infinitely long beam resting on a foundation of finite depth, under a moving force is studied. The effect of foundation inertia is included in the analysis by modelling the foundation as a series of closely spaced axially vibrating rods of finite depth, fixed at the bottom and connected to the beam at the top. Viscous damping in the beam and foundation is included in the analysis. Steady state response of the beam-foundation system is obtained. Detailed numerical results are presented to study the effect of various parameters such as foundation mass, velocity of the moving load, damping and axial force on the beam. It is shown that foundation inertia can considerably reduce the critical velocity and can also amplify the beam response.

Examination of Stress-Fields In Elastic Plastic Indentation

A block of high-purity copper was indented by a 120-degrees diamond-tipped cone. Strain gauges were placed on the surface to measure the radial strains at different surface locations, during loading as well as unloading. The competence of three stress fields proposed for elastic-plastic indentation is assessed by comparing the predicted surface radial strains with those experimentally observed.

Finite element estimation of elastic interlaminar stresses in laminates

Low interlaminar strength and the consequent possibility of interlaminar failures in composite laminates demand an examination of interlaminar stresses and/or strains to ensure their satisfactory performance. As a first approximation, these stresses can be obtained from thickness-wise integration of ply equilibrium equations using in-plane stresses from the classical laminated plate theory. Implementation of this approach in the finite element form requires evaluation of third and fourth order derivatives of the displacement functions in an element. Hence, a high precision element developed by Jayachandrabose and Kirkhope (1985) is used here and the required derivatives are obtained in two ways. (i) from direct differentiation of element shape functions; and (ii) by adapting a finite difference technique applied to the nodal strains and curvatures obtained from the finite element analysis. Numerical results obtained for a three-layered symmetric and a two-layered asymmetric laminate show that the second scheme is quite effective compared to the first scheme particularly for the case of asymmetric laminates.

Coupled electrostatic-elastic analysis for topology optimization using material interpolation

In this paper, we present a novel analytical formulation for the coupled partial differential equations governing electrostatically actuated constrained elastic structures of inhomogeneous material composition. We also present a computationally efficient numerical framework for solving the coupled equations over a reference domain with a fixed finite-element mesh. This serves two purposes: (i) a series of problems with varying geometries and piece-wise homogeneous and/or inhomogeneous material distribution can be solved with a single pre-processing step, (ii) topology optimization methods can be easily implemented by interpolating the material at each point in the reference domain from a void to a dielectric or a conductor. This is attained by considering the steady-state electrical current conduction equation with a `leaky capacitor' model instead of the usual electrostatic equation. This formulation is amenable for both static and transient problems in the elastic domain coupled with the quasi-electrostatic electric field. The procedure is numerically implemented on the COMSOL Multiphysics (R) platform using the weak variational form of the governing equations. Examples have been presented to show the accuracy and versatility of the scheme. The accuracy of the scheme is validated for the special case of piece-wise homogeneous material in the limit of the leaky-capacitor model approaching the ideal case.

Glasslike elastic properties in the omega-beta alloys

We have measured the internal friction and speed of sound in several polycrystalline alloys, using compound torsional oscillators at frequencies between 60 kHz and 100 kHz and temperatures between 50 mK and 100 K. By combining these data with existing elastic and thermal data on similar alloys, we find that those alloys which can undergo diffusionsless phase transitions, such as Ti:Nb, Ti:V, or Zr:Nb in certain ranges of composition have glasslike excitations, since they have elastic properties which agree in magnitude and temperature dependence with those of amorphous solids. By contrast, crystalline continuous solution alloys, such as Nb:Ta, or alloys with diffusive phase transitions, such as high-pressure quenched Al94Si6, have the same elastic properties as are known for crystals.

Use of L matrix to obtain reliable ab initio force constants of polyatomic molecules: ethylene as a test system

Direct use of experimental eigenvalues of the vibrational secular equation on to the ab initio predicted eigenvector space is suggested as a means of obtaining a reliable set of intramolecular force constants. This method which we have termed RECOVES (recovery in the eigenvector space) is computationally simple and free from arbitrariness. The RECOVES force constants, by definition, reproduce the experimental vibrational frequencies of the parent molecule exactly. The ab initio calculations were carried out for ethylene as a test molecule and the force constants obtained by the present procedure also correctly predict the vibrational frequencies of the deuterated species. The RECOVES force constants for ethylene are compared with those obtained by using the SQM procedure.

Calculation of elastic pinning strength of semicoherent Y2BaCuO5 precipitates in YBa2Cu3O7

The pinning energy due to the elastic interaction of a semicoherent Y2BaCuO5 precipitate with the YBa2Cu3O7 matrix is computed. This is achieved by setting up dislocation arrays at the interface. The elastic stresses generated by such arrays are integrated over a fluxoid volume to obtain the energy. It is seen that this elastic interaction energy makes an additive contribution to the total J(c) value.

Nonlinear static and dynamic damped response of a composite rectangular plate resting on a two-parameter elastic foundation

Nonlinear static and dynamic response analyses of a clamped. rectangular composite plate resting on a two-parameter elastic foundation have been studied using von Karman's relations. Incorporating the material damping, the governing coupled, nonlinear partial differential equations are obtained for the plate under step pressure pulse load excitation. These equations have been solved by a one-term solution and by applying Galerkin's technique to the deflection equation. This yields an ordinary nonlinear differential equation in time. The nonlinear static solution is obtained by neglecting the time-dependent variables. Thc nonlinear dynamic damped response is obtained by applying the ultraspherical polynomial approximation (UPA) technique. The influences of foundation modulus, shear modulus, orthotropy, etc. upon the nonlinear static and dynamic responses have been presented.

Interaction analysis of strip footing resting on a non-homogeneous elastic medium

In this paper, a plane stress solution for the interaction analysis of strip footing resting on (i) a non-homogeneous elastic half-plane and (ii) a non-homogeneous elastic layer resting on a rigid stratum has been presented. The analysis has been done using a combined analytical and FEM method in which the discretization of the half-plane is not required and thereby minimizes the computational efforts considerably. The contact pressure distribution and the settlement profile for the selected cases of varying modulus half-plane, which has more relevance to foundation engineering, have been given. Experimental verification through a photoelastic method of stress analysis has been carried out for the case of footing on Gibson elastic half-plane, and the contact pressure distribution thus obtained has been compared with the theoretical results. Copyright (C) 1996 Elsevier Science Ltd

Plates on Elastic Foundation

Analysis of rectangular plates resting on a Winkler-type, one-parameter foundation is studied. The finite element method is applied and a 12-degree-of-freedom, nonconforming rectangular plate element is adopted. Based on shape functions of the plate element, an energy approach is used to derive a closed-form, 12-by-12, consistent foundation stiffness matrix for a rectangular plate on an elastic subgrade. A commonly used method of modeling structural elements on an elastic foundation is the application of discrete springs at the element nodes. The model developed in this paper is compared with the discrete spring model and the convergence of both models is discussed. The convergence of the models is compared with the well-known classical solution of plates on elastic foundation developed in the 1950s. Both models show good convergence to the classical solution. The continuous subgrade response model converges in a manner more consistent with the flexibility of the plate element.

Work fluctuations in an elastic dumbbell model of polymers in planar elongational flow

We use a path-integral approach to calculate the distribution P(w, t) of the fluctuations in the work W at time t of a polymer molecule (modeled as an elastic dumbbell in a viscous solvent) that is acted on by an elongational flow field having a flow rate (gamma) over dot. We find that P(w, t) is non-Gaussian and that, at long times, the ratio P(w, t)/ P (-w, t) is equal to expw/(k(B)T)], independent of (gamma) over dot. On the basis of this finding, we suggest that polymers in elongational flows satisfy a fluctuation theorem.

Reactions of cyanogen radical with alkanes and an explanation for negative temperature dependence of rate constants

Reactions of cyanide radicals with alkanes have been investigated by ab initio methods. It is found that the potential energy surface for reaction of CN with a primary C-H bond in methane has a small positive barrier while reactions of CN with a secondary and a tertiary C-H bond in alkanes are barrierless at the correlated level. A simple explanation for the obtained negative temperature dependence of rate constants for reactions of CN with a secondary and a tertiary C-H bond in alkanes are given in terms of the collision theory of bimolecular reactions. It is shown that for barrierless reactions the negative temperature dependence of the rate constants is attributed to the variation of the pre-exponential factor with temperature.

SCF and electron correlation studies on structure, force constants and vibrational spectra of borane monoammoniate complex

Effects of basis set and electron correlation on the equilibrium geometry, force constants and vibrational spectra of BH3NH3 have been studied. A series of basis sets ranging from double zeta to triple zeta including polarization and diffuse functions have been utilized. All the SCF based calculations overestimate the dative B-N bond distance and considerable improvement occurs when the treatment for electron correlation is introduced. Detailed vibrational analysis for BH3NH3 has been carried out. The mean absolute percentage deviation of the ab initio predicted vibration frequencies of (BH3NH3)-B-11 from the experiment is about 10% for the SCF based calculations and the MP2 method shows better agreement, the overall deviation being 5-6%. The ground state effective force constants of BH3NH3 were obtained using RECOVES procedure. The RECOVES sets of force constants are found to be highly satisfactory for the prediction of the vibrational frequencies of different isotopomers of BH3NH3. The mean absolute percentage deviation of the calculated frequencies of different isotopomers from the experiment is much less than 1%. The RECOVES-MP2/augDZP set of force constants was found to be the best set among the different sets for this molecule. Theoretical infrared intensities are in fair agreement with the observed spectral features.