Preface

Meshfree methods have been developed based on Galerkin type weak formulation and strong formulation with collocation. Galerkin type formulation in conjunction with the compactly supported approximation functions and polynomial reproducibility yields algebraic convergence, while strong form collocation method with nonlocal approximation such as radial basis functions offers exponential convergence. In this work, we discuss rank instability resulting from the nodal integration of Galerkin type meshfree method as well as the ill-conditioning type instability in the radial basis collocation method. We present the recent advances in resolving these difficulties in meshfree methods, and demonstrate how meshfree methods can be applied to problems difficult to be modeled by the conventional finite element methods due to their intrinsic regularity constraints.


Keywords: meshfree methods, stabilization method, collocation method, reproducing kernel, radial basis function.

In this paper an approach of optimization of suspension system parameters is described. Taking into consideration the stiffness and damping coefficients of springs and shock absorbers of a heavy road transport vehicle semitrailer, process of adjusting those values has been undertaken by means of the response surface methodology and a desirability function application, supported by the sensitivity computations. Two different methods of constructing metamodels: Kriging and polynomial regression have been tested and compared with a set of results obtained from the numerical multibody dynamic analysis. The objective of the undertaken efforts was to minimize the loads in the crucial points of the structure, identified as the high-risk failure areas. A number of simulations have been carried out under the set of different load cases, specially established to represent a wide range of operating conditions possible to be met during the vehicle life cycle.


Keywords: multibody modeling, lightweight structures, response surface method, dynamics of multibody system.

Recent developments in Computational Fluid Dynamics (CFD) increased interest in quantifying quality of the numerical models. One of the necessary steps is the so-called code validation procedure, an assessment of a numerical simulation by comparisons between simulation results and laboratory measurements. The focus of the present review is application of modern full field experimental techniques, mostly based on the digital image analysis, in validating numerical solutions of complex flow configurations. Each validation procedure opens new issues of quantifying its outcome to find directions for model updating, limits of computer simulation quality, and to perform uncertainty quantification.


Keywords: CFD validation, experimental methods.

This paper reviews multi-scale computational homogenisation frameworks for the non-linear behaviour of heterogeneous thin planar shells. Based on a review of some of the currently available methods, a computational homogenisation scheme for shells is applied on to representative volume elements for plain weave composites. The effect of flexural loading on the potential failure modes of such materials is analysed, focusing on the reinforcement-matrix delamination mechanism. The attention is next shifted toward failure localisation in masonry unit cells. Subsequently, a recently developed computational FE2 solution scheme accounting for damage localisation at structural scales based on RVE computations is applied.


Keywords: thin planar shells, computational homogenisation, failure, textile reinforced composites, masonry.

The paper addresses various scale-bridging modeling and discretization strategies for multiphase porous materials, starting with a micromechanics model for ion transport within the pore space to generate homogenized diffusion coefficients. Using homogenized macroscopic properties, the theory of poromechanics provides the modeling framework for the macroscopic representation of transport and phase change processes as it is demonstrated for freezing of porous materials using a three-field formulation. The theory of poromechanics is again employed as an appropriate representation of more or less intact porous materials, in conjunction with a two-field Extended Finite Element model as a scale bridging tool to describe coupled hydro-mechanical processes in cracked porous materials at a macroscopic level.


Keywords: micromechanics, poromechanics, Extended Finite Element Method, homogenization, multi-phase models, diffusion, durability, soil freezing.

In this paper we discuss two multi-scale procedures, both of mathematical nature as opposed to purely numerical ones. Examples are shown for the two cases. Attention is also devoted to thermodynamical aspects such as thermodynamic consistency and non-equilibrium thermodynamics. Advances for the first aspect are obtained by adopting the thermodynamically constrained averaging theory TCAT as shown in the case of a stress tensor for multi-component media. The second aspect has allowed to solve numerically, with relative ease, the case of non-isothermal leaching. The absence of proofs of thermodynamic consistency in case of asymptotic theory of homogenization with finite size of the unit cell is also pointed out.


Keywords: multiphysics problems, multi-scale models, asymptotic homogenisation.

The paper deals with transient heat conduction in functionally gradient materials. The spatial variation of the temperature field is approximated by using alternatively two various mesh free approximations, while the time dependence is treated either by the Laplace transform method and/or by the polynomial interpolation in the time stepping method. The accuracy and convergence of the numerical results as well as the computational efficiency of various approaches are compared in numerical test example.


Keywords: heat transfer, boundary value problems, numerical analysis, integral equations, meshless methods.