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Generalized polynomial chaos expansion by reanalysis using static condensation based on substructuring

Applied Mathematics and Mechanics(English Edition) 2024年第5期45卷 819-836页

作者： D.LEE S.CHANG J.LEE Department of Automotive Engineering Hanyang UniversitySeoul 04763Republic of Korea School of Mechanical Engineering Chungnam National UniversityDaejeon 34134Republic of Korea Department of Mechanical Robotics and Energy EngineeringDongguk UniversitySeoul 04620Republic of Korea

This paper presents a new computational method for forward uncertainty quantification(UQ)analyses on large-scale structural systems in the presence of arbitrary and dependent random *** method consists of a generalized polynomial chaos expansion(GPCE)for statistical moment and reliability analyses associated with the stochastic output and a static reanalysis method to generate the input-output data *** the reanalysis,we employ substructuring for a structure to isolate its local regions that vary due to random *** allows for avoiding repeated computations of invariant substructures while generating the input-output data *** substructuring with static condensation further improves the computational efficiency of the reanalysis without losing ***,the GPCE with the static reanalysis method can achieve significant computational saving,thus mitigating the curse of dimensionality to some degree for UQ under high-dimensional *** numerical results obtained from a simple structure indicate that the proposed method for UQ produces accurate solutions more efficiently than the GPCE using full finite element analyses(FEAs).We also demonstrate the efficiency and scalability of the proposed method by executing UQ for a large-scale wing-box structure under ten-dimensional(all-dependent)random inputs.

关键词： forward uncertainty quantification(UQ) generalized polynomial chaos expansion(GPCE) static reanalysis method static condensation substructuring

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p-Multilevel Preconditioners for HHO Discretizations of the Stokes Equations with static condensation

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Communications on Applied Mathematics and Computation 2022年第3期4卷 783-822页

作者： Lorenzo Botti Daniele A.Di Pietro Department of Engineering and Applied Sciences University of BergamoBergamoItaly IMAG Univ MontpellierCNRSMontpellierFrance

We propose a p-multilevel preconditioner for hybrid high-order(HHO)discretizations of the Stokes equation,numerically assess its performance on two variants of the method,and compare with a classical discontinuous Galerkin *** efficient implementa-tion is proposed where coarse level operators are inherited using L2-orthogonal projec-tions defined over mesh faces and the restriction of the fine grid operators is performed recursively and *** h-and k-dependency are investigated tackling two-and three-dimensional problems on standard meshes and graded *** the two HHO for-mulations,featuring discontinuous or hybrid pressure,we study how the combination of p-coarsening and static condensation influences the V-cycle *** particular,two dif-ferent static condensation procedures are considered for the discontinuous pressure HHO variant,resulting in global linear systems with a different number of unknowns and matrix non-zero ***,we show that the efficiency of the solution strategy might be impacted by static condensation options in the case of graded meshes.

关键词： Stokes equations Divergence free constraint Hybrid high-order Discontinuous Galerkin p-multigrid static condensation

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A static condensation Reduced Basis Element Approach for the Reynolds Lubrication Equation

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Communications in Computational Physics 2017年第1期21卷 126-148页

作者： Eduard Bader Martin A.Grepl Siegfried Müller Aachen Institute for Advanced Study in Computational Engineering Science RWTH Aachen UniversitySchinkelstr.252062 AachenGermany Institut für Geometrie und Praktische Mathematik RWTH Aachen UniversityTemplergraben 5552056 AachenGermany

In this paper,we propose a static condensation Reduced Basis Element(SCRBE)approach for the Reynolds Lubrication Equation(RLE).The SCRBEmethod is a computational tool that allows to efficiently analyze parametrized structures which can be decomposed into a large number of similar ***,we extend the methodology to allow for a more general domain decomposition,a typical example being a checkerboard-pattern assembled from similar *** this end,we extend the formulation and associated a posteriori error bound *** motivation comes from the analysis of the pressure distribution in plain journal bearings governed by the ***,the SCRBE approach presented is not limited to bearings and the RLE,but directly extends to other component-based *** show numerical results for plain bearings to demonstrate the validity of the proposed approach.

关键词： Reynolds lubrication equation static condensation domain decomposition model order reduction reduced basis element method a posteriori error estimation

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A New Non-uniform Beam Element and Its Application to Buckling Analysis for Framed Structures

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Journal of Donghua University(English Edition) 2012年第2期29卷 111-114页

作者：陆念力王佳 School of Mechatronics Engineering Harbin Institute of Technology

The non-uniform beam components are commonly used in engineering,while the method to analyze such component is not too satisfactory yet. A new non-uniform beam element with high precision was developed based on the non-linear analysis and the static condensation. Based on the interpolation theory, the displacement fields of the three-node non-uniform Euler-Bernoulli beam element were constructed at first: the quintic Hermite interpolation polynomial was used for the lateral displacement field and the quadratic Lagrange interpolation polynomial for the axial displacement field. Then,based on the basic assumptions of non-uniform Euler-Bernoulli beam whose section properties were continuously varying along its centroidal axis, the linear and geometric stiffness matrices of the three-node non-uniform beam element were derived according to the nonlinear finite element theory. Finally,the degrees of freedom ( DOFs) of the middle node of the element were eliminated using the static condensation method, and a new two-node non-uniform beam element including axial-force effect was obtained. The results indicate that each bar needs to be meshed with only one element could get a fairly accurate solution when it is applied to the stability analyses.

关键词： non-uniform beam element finite element method structural buckling framed structures static condensation

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