Imperfect transmission conditions for a thin weakly compressible interface. 2D problems

New imperfect transmission conditions for a thin nonlinear heat-resistant reactive interphase situated between two different materials are evaluated. The transmission conditions are mathematically derived under a minimum set of assumptions, much less restrictive in comparison with those known in the literature. Numerical simulations based on the finite element method demonstrate the high efficiency of the approach by evaluating the involved error.

Imperfect transmission conditions modelling a thin intermediate layer between two bonded materials in a dissimilar strip are derived in this paper. The interphase material is assumed to be heat-resistant and situated in a thin rectangular domain between the main materials. Different types of the interphase are investigated: homogeneous and inhomogeneous; linear and nonlinear ones.

Imperfect elasticity of materials of interacting sol� ids results in hysteresis losses during their deforma� tion, which, in particular, is the cause of the appear� ance of forces of sliding and rolling friction. One of the most widespread models of an imperfectly elastic material is the viscoelastic solid. The contact problems of the sliding and rolling of linearly viscoelastic solids in the 2�D formulation are considered in (1-8). In these studies, the contact pres� sure distribution, its motionvelocity dependence, and the force of resistance to the motion caused by the relaxation properties of a viscoelastic solid are deter� mined. The class of 3�D contact problems is presented mainly by problems about pressing a stamp (indenter) in a viscoelastic halfspace (9-12). In this study, we proposed a numerical-analytical method of determining the contact pressure distribu� tion and an unknown contact area for the smooth indenter sliding with a constant velocity with zero shear stress at the boundary of the viscoelastic half� space. The problem is solved in the quasistatic formu� lation by constructing the Green's function for the vis� coelastic halfspace (the analogue of the Boussinesq function) for sliding of a concentrated force along it with a constant velocity. The material properties are characterized by the spectrum of relaxation of times. 1. The smooth indenter is loaded by a vertical force Q and moves with a constant velocity V over the vis� coelastic halfspace in the direction of the axis 0x (Fig. 1). The halfspace is described by the coordi� nates |x| < ∞, |y| < ∞, and z ≤ 0. In the mobile Cartesian system of coordinates (

Second order method for solving 3D elasticity equations with complex interfaces

The use of mesh-based numerical methods for a 3D elasticity solution of thick plates involves high computational costs. This particularly limits parametric studies and material distribution design problems because they need a large number of independent simulations to evaluate the effects of material distribution and optimization. In this context, in the current work, the Proper Generalized Decomposition (PGD) technique is adopted to overcome this difficulty and solve the 3D elasticity problems in a high-dimensional parametric space. PGD is an a priori model order reduction technique that reduces the solution of 3D partial differential equations into a set of 1D ordinary differential equations, which can be solved easily. Moreover, PGD makes it possible to perform parametric solutions in a unified and efficient manner. In the present work, some examples of a parametric elasticity solution and material distribution design of multi-directional FGM composite thick plates are presented after some validation case studies to show the applicability of PGD in such problems.

Finite element analysis of laterally loaded fin piles

A stable node-based smoothed PFEM for solving geotechnical large deformation 2D problems

A study is carried out of a thin plate of constant thickness made of linearly elastic material which is transversally isotropic and heterogeneous in the thickness direction. Asymptotic expansions in powers of the relative plate thickness are constructed, and the bending equation of second-order accuracy (the SA model) is delivered. The results of the SA model are compared with the Kirchhoff–Love classical model and with the Timoshenko–Reissner (TR) model, as well as with the exact solution. To this end, some problems for a functionally gradient plate bending, and for a multi-layer plate bending and free vibration are solved and analysed. The range of plate heterogeneity, for which the error of the approximate models is small, is established. The TR model and the SA model are proved to yields results close to each other and the exact results for a very broad range of heterogeneity. That is why the generalized TR model for one-layered homogeneous transversely isotropic plate is proposed. Parameters of this model are chosen so that the results are close to the exact results and the results by the SA model. For the Navier boundary conditions, the analytical solution of 3D problems for a rectangular heterogeneous plate is constructed.

ABSTRACTA predictor–corrector scheme is presented to improve the shape of 3D crack fronts within the 3D simulation of fatigue crack growth. This concept is fully functional for mode‐I, and an extension for mixed‐mode problems is presented. The whole procedure is embedded in an automatic incremental crack growth algorithm for arbitrary 3D problems with linear elastic material behaviour. The numerical simulation is based on the 3D dual boundary element method (Dual BEM) and on an optimized evaluation of very accurate stress intensity factors (SIFs) and T‐stresses. As part of the proposed predictor–corrector scheme, 3D singularities along the crack front especially in the vicinity of the intersection of the crack front and the boundary are considered. The knowledge of these singularities allows the specification of crack front shapes with bounded energy release rate. Numerical examples with complex cross‐sections are presented to show the efficiency of the proposed crack growth algorithm. The obtained results are in good agreement with recent experimental results.