Octavio Andrés González‐Estrada, Juan José Ródenas, Stéphane Pierre Alain Bordas, Marc Duflot, Pierre Kerfriden and Eugenio Giner
The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the singular…
Abstract
Purpose
The purpose of this paper is to assess the effect of the statical admissibility of the recovered solution and the ability of the recovered solution to represent the singular solution; also the accuracy, local and global effectivity of recovery‐based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM).
Design/methodology/approach
The authors study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR‐CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution.
Findings
Numerical results comparing the convergence and the effectivity index of both techniques with those obtained without the enrichment enhancement clearly show the need for the use of extended recovery techniques in Zienkiewicz‐Zhu type error estimators for this class of problems. The results also reveal significant improvements in the effectivities yielded by statically admissible recovered solutions.
Originality/value
The paper shows that both extended recovery procedures and statical admissibility are key to an accurate assessment of the quality of enriched finite element approximations.
Details
Keywords
Shuohui Yin, Tiantang Yu, Tinh Quoc Bui and Minh Ngoc Nguyen
The purpose of this paper is to propose an efficient and accurate numerical model that employs isogeometric analysis (IGA) for the geometrically nonlinear analysis of functionally…
Abstract
Purpose
The purpose of this paper is to propose an efficient and accurate numerical model that employs isogeometric analysis (IGA) for the geometrically nonlinear analysis of functionally graded plates (FGPs). This model is utilized to investigate the effects of boundary conditions, gradient index, and geometric shape on the nonlinear responses of FGPs.
Design/methodology/approach
A geometrically nonlinear analysis of thin and moderately thick functionally graded ceramic-metal plates based on IGA in conjunction with first-order shear deformation theory and von Kármán strains is presented. The displacement fields and geometric description are approximated with nonuniform rational B-splines (NURBS) basis functions. The Newton-Raphson iterative scheme is employed to solve the nonlinear equation system. Material properties are assumed to vary along the thickness direction with a power law distribution of the volume fraction of the constituents.
Findings
The present model for analysis of the geometrically nonlinear behavior of thin and moderately thick FGPs exhibited high accuracy. The shear locking phenomenon is avoided without extra numerical efforts when cubic or high-order NURBS basis functions are utilized.
Originality/value
This paper shows that IGA is particularly well suited for the geometrically nonlinear analysis of plates because of its exact geometrical modelling and high-order continuity.
Details
Keywords
France's new government.
Details
DOI: 10.1108/OXAN-DB208505
ISSN: 2633-304X
Keywords
Geographic
Topical
Kuanfang He, Wei Lu, Xiangnan Liu, Siwen Xiao and Xuejun Li
This paper aims to study acoustic emission (AE) propagation characteristics by a crack under a moving heat source, which mainly provides theoretical basis and method for the…
Abstract
Purpose
This paper aims to study acoustic emission (AE) propagation characteristics by a crack under a moving heat source, which mainly provides theoretical basis and method for the actual crack detection during welding process.
Design/methodology/approach
The paper studied the AE characteristics in welding using thermoelastic theory, which investigates the dynamical displacement field caused by a crack and the welding heating effect. In the calculation model, the crack initiation and extension are represented by moment tensor as the AE source, and the welding heat source is the Gauss heat flux distribution. The extended finite element method (XFEM) is implemented to calculate and solve the AE response of a thermoelastic plate with a crack during the welding heating effect. The wavelet transform is applied to the time–frequency analysis of the AE signals.
Findings
The paper provides insights about the changing rule of the acoustic radiation patterns influenced by the heating effect of the moving heat source and the AE signal characteristics in thermoelastic plate by different crack lengths and depths. It reveals that the time–frequency characteristics of the AE signals from the simulation are in good agreement with the theoretical ones. The energy ratio of the antisymmetric mode A0 to symmetric mode S0 is a valuable quantitative inductor to estimate the crack depth with a certain regularity.
Research limitations/implications
This paper mainly discusses the application of XFEM to calculate and analyze thermoelastic problems, and has presented few cases based on a specified configuration. Further work will focus on the calculation and analysis under different plate configurations and conditions, which is to obtain more interesting and general conclusions for guiding practice.
Originality/value
The paper is a successful application of XFEM to solve the problem of AE response of a crack in the dynamic welding inhomogeneous heating effect. The paper provides an effective way to obtain the AE signal characteristics in monitoring the welding crack.