Adaptive smoothed stable extended finite element method for weak discontinuities for finite elasticity

Jansari, Chintan; Natarajan, Sundararajan; Beex, Lars; Kannan, K.

doi:10.1016/j.euromechsol.2019.103824

Cited by 9 publications

(3 citation statements)

References 49 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…SNMMs and SXFEMs often possess enhanced numerical properties, for example, higher accuracy, convergence, and efficiency. For example, a cell‐based strain smoothing was combined with stable XFEM to strengthen the convergence and efficiency 101 . Wan et al 102 incorporated the strain smoothing technique in XFEM and transformed the domain integrals needed for calculating both stiffness and mass matrices into boundary integrals.…”

Section: Introductionmentioning

confidence: 99%

“…For example, a cell-based strain smoothing was combined with stable XFEM to strengthen the convergence and efficiency. 101 Wan et al 102 incorporated the strain smoothing technique in XFEM and transformed the domain integrals needed for calculating both stiffness and mass matrices into boundary integrals. Jiang et al 103 proposed a SXFEM based on the faced-based strain smoothing for three-dimensional crack analysis.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Preconditioned smoothed numerical manifold methods with unfitted meshes

Liu,

Guan,

Tong

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

The numerical manifold method (NMM) has been widely utilized to solve problems involving complicated boundaries, cracks, and interfaces. Recently, strain or gradient smoothing techniques have been incorporated into NMM to improve its performance. The resulting smoothed NMMs (SNMMs) normally possess enhanced numerical properties, for example, higher accuracy, convergence, and efficiency. A challenging issue rooted in NMM and other enhanced finite element methods using unfitted meshes is the ill‐conditioning induced by extremely small cut element. In this study, we investigate the behaviors of SNMMs in the case of small cut element. It is demonstrated that the cut‐induced ill‐conditionings also exist for two types of SNMMs, namely, edge‐based SNMM and physical‐patch‐based SNMM. Furthermore, a preconditioner based on the normalization of basis functions is proposed to resolve the ill‐conditioning. Several benchmark problems demonstrate the performances of SNMMs regarding accuracy, convergence, and stability.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Preconditioned smoothed numerical manifold methods with unfitted meshes

Liu,

Guan,

Tong

et al. 2023

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…Once strain localisation happens, large strains can accumulate inside a narrow band and eventually lead to fracture (Ortiz et al, 1987;Oliver, 1996;François and Keita, 2015;Tvergaard, 2015). Originated from the traditional FEM methods, the XFEM method is based on the partition of unity method that enriches the FEM shape functions to capture the discontinuities in materials (Belytschko and Black, 1999;Malekan et al, 2018;Jansari et al, 2019). The main advantages of FEM-based fracture models are their high accuracy compared with analytical solutions because the FEM formulation is very versatile in terms of accommodating the implementations of different theoretical models.…”

Section: Introductionmentioning

confidence: 99%

A generic computational model for three-dimensional fracture and fragmentation problems of quasi-brittle materials

Guo

Xiang

Latham

et al. 2020

European Journal of Mechanics - A/Solids

View full text Add to dashboard Cite

Fracture and fragmentation in three dimensions are of great importance to understand the mechanical behaviour of quasi-brittle materials in failure stress states. In this paper, a generic computational model has been developed in an in-house C/C++ code using the combined finite-discrete element method, which is capable of modelling the entire three-dimensional fracturing process, including pre-peak hardening deformation, post-peak strain softening,

show abstract

Design of metamaterial-based heat manipulators using isogeometric level-set topology optimization

Jansari,

Bordas,

Atroshchenko

2024

Struct Multidisc Optim

View full text Add to dashboard Cite

We exploit level-set topology optimization to find the optimal material distribution for metamaterial-based heat manipulators. The level-set function, geometry, and solution field are parameterized using the Non-Uniform Rational B-Spline (NURBS) basis functions to take advantage of easy control of smoothness and continuity. In addition, NURBS approximations can produce conic geometries exactly and provide higher efficiency for higher-order elements. The values of the level-set function at the control points (called expansion coefficients) are utilized as design variables. For optimization, we use an advanced mathematical programming technique, Sequential Quadratic Programming. Taking into account a large number of design variables and the small number of constraints associated with our optimization problem, the adjoint method is utilized to calculate the required sensitivities with respect to the design variables. The efficiency and robustness of the proposed method are demonstrated by solving three numerical examples. We have also shown that the current method can handle different geometries and types of objective functions. In addition, regularization techniques such as Tikhonov regularization and volume regularization have been explored to reduce unnecessary complexity and increase the manufacturability of optimized topologies.

show abstract

Adaptive smoothed stable extended finite element method for weak discontinuities for finite elasticity

Cited by 9 publications

References 49 publications

Preconditioned smoothed numerical manifold methods with unfitted meshes

Preconditioned smoothed numerical manifold methods with unfitted meshes

A generic computational model for three-dimensional fracture and fragmentation problems of quasi-brittle materials

Design of metamaterial-based heat manipulators using isogeometric level-set topology optimization

Contact Info

Product

Resources

About