A hybrid micro–macro BEM formulation for micro-crack clusters in elastic components

Local analysis schemes capable of detailed representations of the micro-features of a problem are integrated with a macro-scale BEM technique capable of handling complex finite geometries and realistic boundary conditions. The micro-scale effects are introduced into the macro-scale BEM analysis through an augmented fundamental solution obtained from an integral equation representation of the micro-scale features. The proposed hybrid micro-macro BEM formulation allows decomposition of the complete problem into two sub-problems, one residing entirely at the micro-level and the other at the macro-level. This allows for investigations of the effects of the micro-structural attributes while retaining the macro-scale geometric features and actual boundary conditions for the component or structure under consideration. As a first attempt, elastic fracture mechanics problems with interacting cracks at close spacings are considered. The numerical results obtained from the hybrid BEM analysis establish the accuracy and effectiveness of the proposed micro–macro computational scheme for this class of problems. The proposed micro–macro BEM formulation can easily be extended to investigate the effects of other micro-features (e.g. interfaces, short or continuous fibre reinforcements, voids and inclusions, in the context of linear elasticity) on macroscopic failure modes observed in structural components.     

A hybrid frequency–time domain method for predicting multiaxial fatigue life of 7075‐T6 aluminium alloy under random loading

A hybrid frequency–time domain method for predicting multiaxial fatigue life under random loading is developed on the basis of combination of the frequency domain and time domain analysis. The critical damage point of the structure is determined by the frequency domain equivalent stress method. Then, the fatigue life prediction is made in time domain by generating random load‐time histories from the power spectral density of the critical point. The method is validated with the random vibration fatigue test of 7075‐T6 aluminium alloy. It has been shown that the results of fatigue life calculated by hybrid method are well correlated with the experiment.     

Improved hybrid displacement function (IHDF) element scheme for analysis of Mindlin–Reissner plate with edge effect

For a Mindlin–Reissner plate subjected to transverse loadings, the distributions of the rotations and some resultant forces may vary very sharply within a narrow district near certain boundaries. This edge effect is indeed a great challenge for conventional finite element analysis. Recently, an effective hybrid displacement function (HDF) finite element method was successfully developed for solving such difficulty 1 , 2 . Although good performances can be obtained in most cases, the distribution continuity of some resulting resultants is destroyed when coarse meshes are employed. Moreover, an additional local coordinate system must be used for avoiding a singular problem in matrix inversion, which makes the derivations more complicated. Based on a modified complementary energy functional containing Lagrangian multipliers, an improved HDF (IHDF) element scheme is proposed in this work. And two new special IHDF elements, named by IHDF‐P4‐Free and IHDF‐P4‐SS1, are constructed for modeling plate behaviors near free and soft simply supported boundaries, respectively. The present modeling scheme not only greatly improves the precision of the numerical results but also avoids usage of the additional local Coordinate system. The numerical tests demonstrate that the new IHDF element scheme is an effective way for solving the challenging edge effect problem in Mindlin–Reissner plates. Copyright © 2016 John Wiley & Sons, Ltd.     

A combined FIC‐TDG finite element approach for the numerical solution of coupled advection–diffusion–reaction equations with application to a bioregulatory model for bone fracture healing

Numerical schemes for the approximative solution of advection–diffusion–reaction equations are often flawed because of spurious oscillations, caused by steep gradients or dominant advection or reaction. In addition, for strong coupled nonlinear processes, which may be described by a set of hyperbolic PDEs, established time stepping schemes lack either accuracy or stability to provide a reliable solution. In this contribution, an advanced numerical scheme for this class of problems is suggested by combining sophisticated stabilization techniques, namely the finite calculus (FIC‐FEM) scheme introduced by Oñate et al. with time‐discontinuous Galerkin (TDG) methods. Whereas the former one provides a stabilization technique for the numerical treatment of steep gradients for advection‐dominated problems, the latter ensures reliable solutions with regard to the temporal evolution. A brief theoretical outline on the superior behavior of both approaches will be presented and underlined with related computational tests. The performance of the suggested FIC‐TDG finite element approach will be discussed exemplarily on a bioregulatory model for bone fracture healing proposed by Geris et al., which consists of at least 12 coupled hyperbolic evolution equations. Copyright © 2012 John Wiley & Sons, Ltd.