Interaction of rocking vibration of a buried rigid circular disc and a two-layer transversely isotropic half-space

AbstractA linear elastic layer of finite thickness bonded on a half-space each containing a transversely isotropic material is considered. A rigid circular disc attached to the interface of these two domains is considered to be affected by a rocking vibration of constant amplitude. With the aid of a scalar potential function, the equations of motion in each domain are solved using Fourier series and Hankel integral transforms. Because of the involved integral transforms, the mixed boundary value problem is changed to dual integral equations; which are reduced to Fredholm integral equations. Because of the complex integrand function existing in the dynamic case, analytical solution cannot be given in general. However, a closed-form solution is introduced for the static case, which itself degenerates to the solution for an isotropic case existing in the literature. The contact stress in between the rigid disc and the surrounding media, and the related impedance function are analytically determined in the static case. With the help of contour integration, the governing Fredholm integral equations are numerically evaluated in the dynamic case. The dynamic contact pressure and the impedance function are numerically evaluated in a general dynamic case. The shape induced singularity in the contact pressure is investigated in detail. Some numerical evaluations are given for different transversely isotropic materials to show the effect of anisotropy

Static analysis of axisymmetric 3-D layered transversely isotropic thick cylindrical shells by displacement potential function

This work considers an effective analytical method based on Displacement Potential Function (DPF) for solving 3-D thick and multi-layered transversely isotropic linearly elastic cylindrical shells (non-homogeneous in radial direction) with simply-supported end boundary conditions. Axisymmetric radial loads are applied on the inner and outer faces of the cylindrical shell. Three-dimensional elasticity equations are simplified using displacement potential function result in one single linear partial differential equation of fourth order as governing differential equation in term of displacement potential function. The governing equation is solved via the separation of variable method with exact satisfaction of two end boundary conditions including stress and displacement boundary conditions, stresses on the inner and outer surfaces of the shell, and the continuity conditions of the displacement and tractions on the interfacial surfaces of the multi-layered cylindrical shell. After determining displacement potential function, all other functions such as stresses and displacements can be obtained at each point of the examined shell. Comparison of the results with existing analytical results show excellent agreement at different thickness ratios and aspect ratios of the shells. Some practical problems are solved for one-layered and three-layered cylindrical shells. For this purpose, three types of materials are defined for a one-layered cylindrical shell such as composite material (Graphite epoxy), metallic substance (e.g. Zinc), and isotropic material (Aluminum). Also two combinations of materials are considered for three-layered cylindrical shell so that the inner and outer layers of the shell are made of transversely isotropic material (Graphite epoxy), while the middle layer of the isotropic material is made of aluminum and foam. The values of the non-dimensional functions containing stress and displacement components are calculated for these problems to demonstrate the effect of thickness ratio and anisotropy of the shell on the distribution of the stresses and displacements

Specimen shape effect on the compressive behavior of PVA fiber-reinforced self-consolidating concrete

The mechanical properties of concrete are dependent on the specimen size and shape. This phenomenon is caused by the heterogeneous nature of concrete and results in significant dissimilarities between the laboratory-made samples and larger concrete elements in the construction fields. Thus, it is required to develop experimental and numerical models to translate the strength of different concrete specimens with varying sizes and shapes. In this research, the effect of specimen shape is evaluated for PVA fiber-reinforced self-consolidating concrete. To do so, three self-consolidating mix proportions were designed, containing two different dosages of PVA fibers and various sizes of cylindrical and cubic specimens were cast in order to account for the influence of specimen size and geometry. The fresh properties of the designed SCC concretes were assessed using several experiments such as slump flow time and diameter tests, V-funnel flow time test, and L-box test. Also, the 28-day compressive strength of the designed samples was obtained using a pressure jack. The specimen shape and size effect of PVA fiber-reinforced self-consolidating concrete was studied based on specimen geometry and fracture mechanism, and the influence of PVA fiber addition on the compressive strength of samples was presented in the form of linear equations. By analyzing the obtained data, relations were proposed to translate the strength of cylindrical specimens to cubic specimens. Also, for the first time, the experimental coefficients of Bazant's model were achieved for PVA fiber-reinforced SCC, and the Bazant's size effect model became functional for the designed concretes. To do so, non-linear regression analysis was conducted on the obtained experimental data. According to the achieved results, the addition of 0.08% of PVA fibers increased the transitional size coefficient (D0) of cylindrical and cubic specimens by 170.39% and 105.86%, respectively, reduced the size effect, and enhanced the ductility in the designed self-consolidating concretes

Analytical Solution for a Two-Layer Transversely Isotropic Half-Space Affected by an Arbitrary Shape Dynamic Surface Load

The dynamic response of a transversely isotropic, linearly elastic layer bonded to the surface of a half-space of a different transversely isotropic material under arbitrary shape surface loads is considered. With the help of displacements and stresses Green’s functions, an analytical formulation is presented for the determination of the displacements and stresses at any point in both surface layer and the underneath half-space in frequency domain. Special results are prepared for circular, ellipsoidal, square and recangular patch load. It is shown that the displacements and stresses due to circular patch load are colapesd on the existing solution in the literature. Some new illustrations are prepared to show the effect of the shape of the patch on the responses of the domain specially near the load

A tri-material elastodynamic solution for a transversely isotropic full-space

AbstractA linear elastic full-space composed of an upper half-space, a lower half-space and a layer of three different transversely isotropic materials under an internal load is considered. The axes of symmetry of the different regions are assumed to be normal to the planar interfaces of the regions and are thus parallel. An arbitrary load in the frequency domain is allowed on a finite patch located at the interface of the upper half-space and the adjacent layer. By means of the complete displacement potentials, the displacements and stresses in the three regions are determined in Fourier–Hankel space in the form of line integrals. The solution can be degenerated to the solution for (i) a full-space under an arbitrary buried load, (ii) a half-space contain a layer bonded to the top of it under an arbitrary surface force, (iii) a half-space under an arbitrary surface load, (iv) a two layer half-space under an arbitrary force applied at the interface of two regions, (v) a half-space under an arbitrary buried force, (vi) a layer of finite thickness fixed at the bottom and under an arbitrary surface load, and (vii) a bi-material full-space under an arbitrary load at the interface of two materials. Examples of the displacements and stresses are obtained numerically and compared to existing solutions