In this investigation, the general formalism for the field equations governing the dynamic response of fluid-saturated porous media is analyzed and employed for the study of transient wave motion. The two constituents are assumed to be incompressible. A one-dimensional analytical solution is derived by means of Laplace transform technique which, as a result of the incompressibility constraint, exhibits only one independent dilatational wave propagating in the solid and the fluid phases, respectively. The fluid-saturated porous material is supplied with characteristics similar to those occuring in viscoelastic solids. This work can provide the further understanding of the characteristics of wave propagation in porous materials and may be taken for a quantitative comparision to various numerical solutions.
The paper presents a finite element model of the rectangular plate with a through crack. The crack occurring in the plate is nonpropagating and open. It was assumed that the crack changes only the stiffness of the plate, whereas the mass is unchanged. The method of the formation of the stiffness matrix of a finite element for the rectangular, cracked plate is presented. The effects of the crack location and its length on the changes of the eigenfrequencies of the simply supported and cantilever plate are studied. The results of numerical computations are compared with results of theoretical and experimental data presented in the literature.
In multibody dynamics, topology variations are caused by the fact that bodies, that are initially separated from one another, get into contact and slide or roll along each other under the influence of friction. These topology variant systems are characterized by the fact that, during the evolution in time, their number of degrees of freedom changes by latent constraints becoming active or passive due to and controlled by the system dynamics itself. In studying such systems, the following procedure is selected: With a system description in minimal coordinates without use of latent constraints, the constraints that are indicated as being potentially active by the evaluation of kinematic indicators, in this case being relative velocity and distance, are considered as algebraic secondary conditions and are taken into account by including Lagrange multipliers in the equation of motion. A sufficient condition for all potentially active constraints to remain active or become passive is provided by the solution of a complementarity problem that, in a planar case, is linear and argues at acceleration level by self-excluding kinetic indicators.
Within the framework of linear-elastic classical laminated plate theory, the problem of an elliptical hole in.an infinitely extended unsymmetric laminate is treated. For the underlying non-symmetric layup arbitrary bending extension coupling is admitted and is taken into account by means of a new complex potential approach. The corresponding analytical solution is given for the case of homogeneous in-plane and bending loading of the laminate. The derived solution describes all essential plate quantities in any vicinity of the elliptical hole and it reveals interesting features of the considered bending extension coupling.
Based on Tresca's yield criterion and the associated flow rule, the thermal assembly of an elastic-plastic hollow cylinder and a solid shaft is investigated. The transient stress distribution in the shrink fit is discussed and illustrated by numerical results.
The buckling problem of thick circular plates under uniform radial loads with allowance for inplane prebuckling deformation is solved analytically. The analytical buckling solutions should be very useful as benchmark values for testing the validity, convergence and accuracy of numerical techniques for plate buckling. This study shows the importance of including the prebuckling deformation in thick plate buckling since its effect is in the same order of magnitude as that of shear. The prebuckling deformation effect raises the critical load and is more pronounced in clamped plates than in simply supported ones as the former plates undergo greater deformation before buckling.
Based on the classical stress analysis, the stress field of a screw dislocation near a semi-infinite crack is investigated by a conformal mapping method. The classical image force on the dislocation due to the crack is presented by the obtained classical image stress. To eliminate the singularity of the stress field at the crack tip, the nonlocal elasticity theory is adopted. A maximum of the image stress is found near the crack tip and the nonlocal image force is then acquired by the obtained nonlocal stress field. Both the stress and the image force show much difference from the classical ones and seem to be more reasonable physically.
This paper is concerned with finite deformations of elastic bodies in the presence of unilateral constraints. The penalty formulation is applied to introduce the contact constraints. We develop special isoparametric contact elements. Starting from their Gaussian points the distance between the body and the obstacle is determined, where the obstacle is given as a C2 continuous function. Variation and subsequent consistent linearization yield the tangent matrix of the contact elements in its general form, which can be incorporated into standard finite element schemes.
Martensitic transformation behavior of alloys is studied under the arbitrary action of a thermal and/or a triaxial mechanical load-stress state by solving a transformation kinetic equation presented recently by the same authors. Numerical and analytical solutions reveal that the transformation behavior is almost path-independent. Lines of constant volume fraction of martensite are nearly parallel in the stress-temperature plane. Some new analytical formulae for martensitic transformation kinetics are presented.
An investigation is made of the phenomena occurring at the contact of elastic spheres, subjected to forces with varying tangential component, in one direction, with changing sign, and varying normal component. The contact law is based on the assumption, introduced by H. Hertz , that both bodies behave physically like elastic half-spaces. We assume constant stress directions in the slip area in order to use so-called Cattaneo-Mindlin functions to solve the tangential boundary value problem. The stress distribution of the Cattaneo-Mindlin theory ,  is rotational symmetric and has a typical break at the border of the stick area at rho = a1*, for al* < a1, with the radius a1* of the stick area and the radius a1 of the contact area. The general solution of the tangential contact problem can be written as a sum of Cattaneo-Mindlin functions. The appropriate superposition of two Cattaneo-Mindlin functions yields a new Cattaneo-Mindlin function, which simplifies the calculation of the force and the displacement. We will arrive at a formula for the force-displacement relation of general load-histories, which can be reduced to the compliances of Mindlin & Deresiewicz  by differentiation. In contrast to Mindlin & Deresiewicz our formula depends only on the points of instantaneous adhesion P(i), for 1 less-than-or-equal-to i less-than-or-equal-to N - 1, and the current displacements xi(N), zeta(N) in tangential and normal direction of the initial contact point, which simplifies the solution. It also allows a generalization for oblique load-histories with elliptical contact areas and tangential forces in varying directions . Finally an algorithm is given, which determines the essential number of Cattaneo-Mindlin functions.
Coriolis flowmeters are essentially fluid conveying pipe segments excited to transversal oscillation. Thereby the precise form of the oscillation modes depends on the mass flow rate Q(M) of the fluid. For usual flow rates the modes deviate only slightly from those without flow (Q(M) = 0); they can be viewed as small perturbations of those modes. In the paper it is shown that the perturbation of a given oscillation mode of the pipe segment by the fluid flow, which manifests itself as a slight tumbling of the pipe segment, can be interpreted as a mixing of this (working) mode with its (spectral) neighbours. The tumbling in the perturbed mode comes out thereby roughly as an interplay of neighbouring unperturbed modes, with a phase difference of 90-degrees. The mode interference depends strongly on the distance of the involved modes. This suggests a way to increase the sensitivity of the instrument by appropriately influencing the vibration spectrum of the pipe segment, e.g. through change of its geometry.
The unsteady free convection boundary layer at the stagnation point of a two-dimensional body and an axisymmetric body with prescribed surface heat flux or temperature has been studied. The magnetic field is applied parallel to the surface and the effect of induced magnetic field has been considered. It is found that for certain powerlaw distribution of surface heat flux or temperature and magnetic field with time, the governing boundary layer equations admit a self-similar solution locally. The resulting nonlinear ordinary differential equations have been solved using a finite element method and a shooting method with Newton's corrections for missing initial conditions. The results show that the skin friction and heat transfer coefficients, and x-component of the induced magnetic field on the surface increase with the applied magnetic field. In general, the skin friction, heat transfer and x-component of the induced magnetic field for axisymmetric case are more than those of the two-dimensional case. Also they change more when the surface heat flux or temperature decreases with time than when it increases with time. The skin friction, heat transfer and x-component of the induced magnetic field are significantly affected by the magnetic Prandtl number and they increase as the magnetic Prandtl number decreases. The skin friction and x-component of the magnetic field increase with the dissipation parameter, but heat transfer decreases.
The present paper discusses certain methods which permit us to consider the influence of the fractal geometry and the fractal material behaviour in solid and structural mechanics. The method of fractal interpolation function is introduced and the fractal quantities (boundary geometry, interface geometry and stress-strain laws) are considered as the fixed points of a given set-valued transformation. Our first aim here is to define the mechanical quantities on fractal sets using some elementary results of the theory of Besov spaces. Then we try to extend the classical finite element method for the case of fractal bodies and fractal boundaries and corresponding error estimates are derived. The fractal analysis permits the formulation and the treatment of complicated or yet unsolved problems in the theory of deformable bodies.
Analysis of the in plane lateral collapse of square and rectangular cross-section tubes is presented by considering the out-of-straightness of horizontal and vertical arms, corner radius, friction between the platens and the deforming specimen and instability of vertical arms. Results of collapse load for tubes of aluminium and mild steel, thus computed, are presented for some typical tube geometrics, and influence thereon of various parameters considered is discussed. Experiments were conducted wherein tubes of square and rectangular cross-sections of both the materials were laterally compressed between two parallel platens in an Instron machine. The observed collapse loads compare very well with the corresponding computed values.
A hyperelastic constitutive model for compressible materials undergoing large deformations is introduced from the evaluation, by homogenization, of the strain energy density function of periodic porous rubber composites. For infinitesimal deformations the proposed material model remains unidentifiable from the Blatz-Ko one, but it is shown that, at higher stretching levels, these models differ substantially.
It is well known that shell theories, which incorporate shear deformations assuming a linear displacement function in shell thickness direction, can be applied to isotropic problems leading to good results, if a constant shear correction factor with a value of 5/6 is used. For layered cross sections with anisotropic material these simple displacement and strain assumptions are too crude. Thus modifications of correction factors are necessary to adjust the transversal stiffness, if the linear displacement function is applied. The present study shows an improved analysis of a priori calculated shear correction factors for the analysis of shell structures with layered anisotropic cross sections. The theoretical concept is presented and the influence of the new added components is compared on the basis of some numerical examples. The numerical analysis is performed using a bilinear shell element with separate trial functions for the transversal shear strains [6, 1]. This element is implemented into the FE package FEAP  and is further developed for layered anisotropic materials .
The paper deals with a numerical method combining a characteristic-based scheme and Zwas' method in order to solve the hyperbolic PDE's of elastic and elastic-plastic anti-plane shear waves in two space dimensions. First, the need of new physically reasonable numerical methods for stress waves in solids is demonstrated by numerical applications to problems with impulsive loading, where defects of some standard methods are shown. Then, the new secon-dorder accurate method is derived. A suitable procedure to model the elastic-plastic behaviour of materials by simple waves is included. The capability of the methods is demonstrated by application to several examples. Additionally, for comparison with numerical results, a similarity solution for the semi-infinite crack undergoing an elastic-plastic shock loading is derived in the appendix.
Thermal stresses around two parallel cracks in two bonded dissimilar elastic half-planes are determined. One of the cracks lies in the upper half-plane, while the other is in the lower half-plane. Uniform heat flow is assumed to be at right angles to the interface. Application of the Fourier transform technique reduces the problem to that of solving dual integral equations. To solve the equations, the difference of the crack surface temperature and those of the crack surface displacements are expanded in a series of functions which are automatically zero outside the cracks. The unknown coefficients in the series are solved by the Schmidt method. The stress intensity factors are calculated numerically for composite materials featuring a ceramic upper half-plane and a steel lower half-plane.
A family of sensors which measure the complex coefficient of dynamic viscosity (eta*) is discussed. Using a first order approximation to a general viscoelastic fluid, it is shown how these instruments determine eta* for a general linear viscoelastic fluid. The measurement technique employed relates the linear viscous damping and resonant frequency of these instruments in the presence and absence of fluid to eta*. This analysis also provides the inherent limitations of the sensors.