An efficient nonlinear octree SBFEM and its application to complicated geotechnical structures

Chen, Kai; Zou, Degao; Kong, Xianjing; Yu, Xiang

doi:10.1016/j.compgeo.2017.10.021

Cited by 71 publications

(16 citation statements)

References 39 publications

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“…The usual procedure for the construction of SBFEM shape functions is the determination of analytic eigenfunctions for the SBFEM equation (15). We have shown in the previous section that there is another characterization of these shape functions that are not well recognized.…”

Section: Intrinsic Gradient Orthogonality Property For S K (S)mentioning

confidence: 99%

“…Notice that the desired orthogonality property ( 20) is valid for ψ ∈ D 0 (S), with ψe (ξ, η) = C σ(ξ) in the sectors K e , if and only if it holds for functions ϕ = ψ − C σ(1) ∈ D 0 0 (S), i.e., for the cases where φ(ξ) = C(σ(ξ) − σ(1)), with φ(1) = 0. For them, we apply equation (15), valid for all shape functions φ i ∈ S k (S), to reduce the equation ( 14) to…”

Section: Intrinsic Gradient Orthogonality Property For S K (S)mentioning

confidence: 99%

“…More recently, the method has been applied to highly irregular and heterogeneous domains due to the flexibility in generating SBFEM meshes [12,13]. For instance, the SBFEM has been applied in quadtree and octree meshes since hanging nodes can be avoided due to the flexible topology of SBFEM polygonal/polyhedral subregions [14,15,10].…”

Section: Introductionmentioning

confidence: 99%

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Error estimates for the Scaled Boundary Finite Element Method

Coelho,

Devloo,

Gomes

2020

Preprint

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The Scaled Boundary Finite Element Method (SBFEM) is a technique in which approximation spaces are constructed using a semi-analytical approach. They are based on partitions of the computational domain by polygonal/polyhedral subregions, where the shape functions approximate local Dirichlet problems with piecewise polynomial trace data. Using this operator adaptation approach, and by imposing a starlike scaling requirement on the subregions, the representation of local SBFEM shape functions in radial and surface directions are obtained from eigenvalues and eigenfunctions of an ODE system, whose coefficients are determined by the element geometry and the trace polynomial spaces. The aim of this paper is to derive a priori error estimates for SBFEM's solutions of harmonic test problems. For that, the SBFEM spaces are characterized in the context of Duffy's approximations for which a gradient-orthogonality constraint is imposed. As a consequence, the scaled boundary functions are gradient-orthogonal to any function in Duffy's spaces vanishing at the mesh skeleton, a mimetic version of a well-known property valid for harmonic functions. This orthogonality property is applied to provide a priori SBFEM error estimates in terms of known finite element interpolant errors of the exact solution. Similarities with virtual harmonic approximations are also explored for the understanding of SBFEM convergence properties. Numerical experiments with 2D and 3D polytopal meshes confirm optimal SBFEM convergence rates for two test problems with smooth solutions. Attention is also paid to the approximation of a point singular solution by using SBFEM close to the singularity and finite element approximations elsewhere, revealing optimal accuracy rates of standard regular contexts.

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Section: Intrinsic Gradient Orthogonality Property For S K (S)mentioning

confidence: 99%

Section: Intrinsic Gradient Orthogonality Property For S K (S)mentioning

confidence: 99%

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Error estimates for the Scaled Boundary Finite Element Method

Coelho,

Devloo,

Gomes

2020

Preprint

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“…Several authors have combined SBFEM and the octree technique to overcome the limitations of element shape with conventional numerical methods . Figure b shows that the flexible, diverse octree elements can process an arbitrary complicated polyhedron and implement the cross‐scale transition efficiently and smoothly.…”

Section: Containment Vessel Modelmentioning

confidence: 99%

“…This paper combines the scaled boundary polyhedron finite element analysis method with the octree technique to refine the nuclear engineering damage evolution analysis and establish a refined NPP finite element model. First, the sensitivity of the impact and transition area mesh size was discussed.…”

Section: Introductionmentioning

confidence: 99%

A cross‐scale refined damage evolution analysis of large commercial aircraft crashing into a nuclear power plant

Zou

Sui

Chen

et al. 2019

Structural Design Tall Build

Self Cite

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Since the 9/11 attacks, whether nuclear power plants (NPPs) can withstand the malicious impact of large commercial aircraft has become a question that must be considered in the design phase. Refined model and fine-scale element reflect more accurately the failure procedure and behaviour. However, due to the exceedingly complex structure of NPP, the traditional meshing method requires a substantial number of geometric operations involving point, line, area, and volume, leading to a tedious modelling process and very high computational costs, as well as making it difficult to modify and optimize the model. This paper combines the scaled boundary finite element method with the octree technique to refine nuclear engineering damage evolution analysis and establish a refined numerical model of the Generation III + NPP, considering the detailed equipment hatch, air intake, and internal steel containment vessel structures. Subsequently, the refined damage evolution analysis of a large commercial aircraft crashing into an NPP was developed. The mesh size sensitivity, impact region shape comparison, and the influence of different impact heights were discussed. The results indicate that the cross-scale refined meshing and analysis method provides a high-quality discrete grid with fewer elements. Furthermore, this method is highly flexible, more accurately simulating the damage evolution and gradual destruction process. We recommend future structural optimization for the air intake and conducting detailed analyses at this location. The cross-scale analysis method presented in this paper enables a rapid, refined simulation of a malicious impact by a large commercial aircraft. Additionally, it provides technical support for future studies of the responses of NPPs' internal structures, systems, and equipment under extreme earthquake and other disaster conditions. KEYWORDS aircraft crash, Ap1000, damage propagation, polyhedron fine-scale analysis, scaled boundary finite element method (SBFEM)

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The pixel-based quadtree SBFEM with the parameter level set method for identifying cracks and voids

Sun

Peng

et al. 2022

Comput Mech

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An efficient nonlinear octree SBFEM and its application to complicated geotechnical structures

Cited by 71 publications

References 39 publications

Error estimates for the Scaled Boundary Finite Element Method

Error estimates for the Scaled Boundary Finite Element Method

A cross‐scale refined damage evolution analysis of large commercial aircraft crashing into a nuclear power plant

The pixel-based quadtree SBFEM with the parameter level set method for identifying cracks and voids

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