扩展有限元法在线弹性断裂力学中的应用研究

采用改进的XFEM对有限板单边裂纹的应力强度因子和Ⅰ型裂纹的扩展进行分析，数值计算结果表明了该方法的有效性，从而避免了常规有限元方法中的网格重构，大大简化了裂纹扩展的分析过程。     

适用于扩展有限元裂缝计算的钢筋与混凝土粘结滑移关系

以定量分析钢筋与混凝土粘结滑移关系为目标,利用RCXFEHohai-P扩展有限元程序,计算采用不同粘结滑移公式时钢筋混凝土简支梁的最大裂缝宽度。结果表明,计算所得最大裂缝宽度各不相同,且都与《混凝土结构设计规范》(GB 50010—2010)所列最大裂缝宽度公式计算值存在差别。为此,基于GA-BP神经遗传网络,以规范最大裂缝宽度公式计算值为预测目标,反演得到适用于扩展有限元裂缝计算的粘结滑移公式,算例表明该公式能满足扩展有限元裂缝宽度计算要求。研究成果对提高扩展有限元裂缝分析的准确性具有一定的参考价值。     

Augment low-field intra-operative MRI with preoperative MRI using a hybrid non-rigid registration method

Background

Preoperatively acquired diffusion tensor image (DTI) and blood oxygen level dependent (BOLD) have been proved to be effective in providing more anatomical and functional information; however, the brain deformation induced by brain shift and tumor resection severely impairs the correspondence between the image space and the patient space in image-guided neurosurgery.

Method

To address the brain deformation, we developed a hybrid non-rigid registration method to register high-field preoperative MRI with low-field intra-operative MRI in order to recover the deformation induced by brain shift and tumor resection. The registered DTI and BOLD are fused with low-field intra-operative MRI for image-guided neurosurgery.

Results

The proposed hybrid registration method was evaluated by comparing the landmarks predicted by the hybrid registration method with the landmarks identified in the low-field intra-operative MRI for 10 patients. The prediction error of the hybrid method is 1.92 ± 0.54 mm, and the compensation accuracy is 74.3 ± 5.0%. Compared to the landmarks far from the resection region, those near the resection region demonstrated a higher compensation accuracy (P-value = .003) although these landmarks had larger initial displacements.

Conclusions

The proposed hybrid registration method is able to bring preoperatively acquired BOLD and DTI into the operating room and compensate for the deformation to augment low-field intra-operative MRI with rich anatomical and functional information.     

A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers

We present a sweeping window method in elastodynamics for detection of multiple flaws embedded in a large structure. The key idea is to measure the elastic wave propagation generated by a dynamic load within a smaller substructural detecting window domain, given a sufficient number of sensors. Hence, rather than solving the full structure, one solves a set of smaller dynamic problems quickly and efficiently. To this end, an explicit dynamic extended FEM with circular/elliptical void enrichments is implemented to model the propagation of elastic waves in the detecting window domain. To avoid wave reflections, we consider the window as an unbounded domain with the option of full‐infinite/semi‐infinite/quarter‐infinite domains and employ a simple multi‐dimensional absorbing boundary layer technique. A spatially varying Rayleigh damping is proposed to eliminate spurious wave reflections at the artificial model boundaries. In the process of flaw detection, two phases are proposed: (i) pre‐analysis—identification of rough damage regions through a data‐driven approach, and (ii) post‐analysis‐–identification of the true flaw parameters by a two‐stage optimization technique. The ‘pre‐analysis’ phase considers the information contained in the ‘pseudo’ healthy structure and the scattered wave signals, providing an admissible initial guess for the optimization process. Then a two‐stage optimization approach (the simplex method and a damped Gauss–Newton algorithm) is carried out in the ‘post‐analysis’ phase for convergence to the true flaw parameters. A weighted sum of the least squares, of the residuals between the measured and simulated waves, is used to construct the objective function for optimization. Several benchmark examples are numerically illustrated to test the performance of the proposed sweeping methodology for detection of multiple flaws in an unbounded elastic domain. Copyright © 2015 John Wiley & Sons, Ltd.     

On computational homogenization of microscale crack propagation

The effective response of microstructures undergoing crack propagation is studied by homogenizing the response of statistical volume elements (SVEs). Because conventional boundary conditions (Dirichlet, Neumann and strong periodic) all are inaccurate when cracks intersect the SVE boundary, we herein use first order homogenization to compare the performance of these boundary conditions during the initial stage of crack propagation in the microstructure, prior to macroscopic localization. Using weakly periodic boundary conditions that lead to a mixed formulation with displacements and boundary tractions as unknowns, we can adapt the traction approximation to the problem at hand to obtain better convergence with increasing SVE size. In particular, we show that a piecewise constant traction approximation, which has previously been shown to be efficient for stationary cracks, is more efficient than the conventional boundary conditions in terms of convergence also when crack propagation occurs on the microscale. The performance of the method is demonstrated by examples involving grain boundary crack propagation modelled by conventional cohesive interface elements as well as crack propagation modelled by means of the extended finite element method in combination with the concept of material forces. © 2016 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd.     

The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns

A new method for treating arbitrary discontinuities in a finite element (FE) context is presented. Unlike the standard extended FE method (XFEM), no additional unknowns are introduced at the nodes whose supports are crossed by discontinuities. The method constructs an approximation space consisting of mesh‐based, enriched moving least‐squares (MLS) functions near discontinuities and standard FE shape functions elsewhere. There is only one shape function per node, and these functions are able to represent known characteristics of the solution such as discontinuities, singularities, etc. The MLS method constructs shape functions based on an intrinsic basis by minimizing a weighted error functional. Thereby, weight functions are involved, and special mesh‐based weight functions are proposed in this work. The enrichment is achieved through the intrinsic basis. The method is illustrated for linear elastic examples involving strong and weak discontinuities, and matches optimal rates of convergence even for crack‐tip applications. Copyright © 2006 John Wiley & Sons, Ltd.     

Three‐dimensional integration strategies of singular functions introduced by the XFEM in the LEFM

The use of the extended finite element method in the scope of linear elastic fracture mechanics induces the integration of singular functions in terms of the stiffness matrix and in the computation of stress intensity factors using the interaction integral method. An adapted method is proposed in this paper to treat efficiently the three‐dimensional case. The improvement is demonstrated by comparison with standard and other methods found in the literature. Copyright © 2012 John Wiley & Sons, Ltd.     

An extended stochastic pseudo-spectral Galerkin finite element method (XS-PS-GFEM) for elliptic equations with hybrid uncertainties

Nouy and Clement introduced the stochastic extended finite element method to solve linear elasticity problem defined on random domain. The material properties and boundary conditions were assumed to be deterministic. In this work, we extend this framework to account for multiple independent input uncertainties, namely, material, geometry, and external force uncertainties. The stochastic field is represented using the polynomial chaos expansion. The challenge in numerical integration over multidimensional probabilistic space is addressed using the pseudo-spectral Galerkin method. Thereafter, a sensitivity analysis based on Sobol indices using the derived stochastic extended Finite Element Method solution is presented. The efficiency and accuracy of the proposed novel framework against conventional Monte Carlo methods is elucidated in detail for a few one and two dimensional problems.     

Extended finite element method for plastic limit load computation of cracked structures

The extended finite element method is extended to allow computation of the limit load of cracked structures. In the paper, it is demonstrated that the linear elastic tip enrichment basis with and without radial term may be used in the framework of limit analysis, but the six‐function enrichment basis based on the well‐known Hutchinson–Rice–Rosengren asymptotic fields appears to be the best. The discrete kinematic formulation is cast in the form of a second‐order cone problem, which can be solved using highly efficient interior‐point solvers. Finally, the proposed numerical procedure is applied to various benchmark problems, showing that the present results are in good agreement with those in the literature. Copyright © 2015 John Wiley & Sons, Ltd.