Efficient Inelasticity-Separated Finite-Element Method for Material Nonlinearity Analysis

Li, Gang; Yu, Ding‐Hao

doi:10.1061/(asce)em.1943-7889.0001426

Cited by 33 publications

(29 citation statements)

References 27 publications

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“…Therefore, the error stemming from the linearization of the propose scheme in each iteration step is greater than that using the classical full Newton‐Raphson scheme, and more iteration steps are needed for achieving convergence. It has been validated by Li and Yu that the accuracy level of the IS‐FEM is the same to the classical finite element scheme. As far as the proposed scheme is concerned, although the additional error is introduced into the solution of Woodbury formula per iteration, the increase in iteration steps for achieving convergence can minimize the effect of this kind of error on accuracy level of the final results.…”

Section: Inelasticity‐separated Rc Fiber Beam‐column Modelmentioning

confidence: 97%

“…Through decomposing the nonlinear strain of material into linear‐elastic and inelastic components according to initial material modulus and treating the separated inelastic strain as additional DOFs, the IS‐FEM proposed by Li and Yu is capable to keep the global stiffness matrix of a structure unchanged during the whole computation process and separate the coefficient matrices with small rank representing local material nonlinearity from the global system. Then, the tangent stiffness matrix in classical approach can be transformed into the form of low‐rank modification to the unchanging stiffness matrix, and the Woodbury formula can be applied to improve the computational efficiency of local material nonlinear analysis.…”

Section: Background Of Is‐femmentioning

confidence: 99%

“…Based on the inelasticity‐separated concept, the section deformation vector Δ d in can be decomposed into linear‐elastic and inelastic components according to initial section stiffness, ie,

Δ d_{in} = Δ d_{in}^{'} + Δ d_{in}^{″},

where

Δ d_{in}^{'}

is incremental linear‐elastic section deformation that is equal to the corresponding initial section flexibility matrix (ie, the inverse of initial section stiffness) multiplied by the incremental section forces Δ m in ;

Δ d_{in}^{″}

is incremental inelastic deformation that is defined as the difference between total section deformation increment Δ d in and the linear‐elastic section deformation increment

Δ d_{in}^{'}

. Thus, the incremental section forces can also be expressed by

([], \begin{array}{c} Δ m_{in} \\ Δ m_{ela} \end{array}) = D_{e} ([], \begin{array}{c} Δ d_{in}^{'} \\ Δ d_{ela} \end{array}) = ([], \begin{array}{c} D_{italicin, e} & bold0 \\ bold0 & D_{ela} \end{array}) ([], \begin{array}{c} Δ d_{in}^{'} \\ Δ d_{ela} \end{array}) = ([], \begin{array}{c} D_{italicin, e} & bold0 \\ bold0 & D_{ela} \end{array}) ((), ([], \begin{array}{c} Δ d_{in} \\ Δ d_{ela} \end{array}) - ([], \begin{array}{c} Δ d_{} \end{array}))

…”

Section: Inelasticity‐separated Rc Fiber Beam‐column Modelmentioning

confidence: 99%

“…For a given element, the principle of virtual work can be expressed by

l \int_{0}^{1} ((), δ d_{in}^{T} normalΔ m_{in} + δ d_{ela}^{T} normalΔ m_{ela}) italicdξ - δ q^{T} normalΔ boldf = 0,

where δ d in and δ d ela are vectors of virtual section deformation; δ q is the vector of virtual nodal displacement and Δ f is the vector of nodal loads increment. Assume that both collocation points of the element have severe inelasticity level in a certain iteration step, then, by substituting Equations , , , and into and considering Equation , the governing equation of element with incremental form can be derived as

([], \begin{array}{c} boldk & k^{'} \\ {boldk}^{'}^{T} & k_{in}^{″} \end{array}) ([], \begin{array}{c} Δ boldq \\ - Δ {\overset{true¯}{d^{″}}}_{in} \end{array}) = ([], \begin{array}{c} normalΔ boldf \\ bold0 \end{array}),

in which

boldk = l \int_{0}^{1} B^{T} D_{e} boldB italicdξ k^{'} = l \int_{0}^{1} B_{in}^{T} D_{italicin, e} boldC italicdξ k_{in}^{″} = l \int_{0}^{1} C^{T} D_{italicin, e} {({boldD}_{in, e} - {boldD}_{in, t})}^{-}

…”

Section: Inelasticity‐separated Rc Fiber Beam‐column Modelmentioning

confidence: 99%

“…Based on the inelasticity-separated concept, 21 the section deformation vector Δd in can be decomposed into linear-elastic and inelastic components according to initial section stiffness, ie,…”

Section: Section Deformation Decompositionmentioning

confidence: 99%

See 4 more Smart Citations

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

Yu²

2018

Earthq Engng Struct Dyn

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Summary Evaluating the inelastic seismic response of structures accurately is of great importance in earthquake engineering and generally requires refined simulation, which is a time‐consuming process. Because the material nonlinearity generally occurs in a small part of the whole structure, many researches focus on taking advantage of this characteristic to improve the computational efficiency and the inelasticity‐separated finite element method (IS‐FEM) proposed recently provide a generic finite element formulation for solving this kind of problems efficiently. Although the fiber beam‐column element is widely used for the simulation of reinforced concrete (RC) framed structures, the inelastic deformation is often detected in a large part of the numerical model under earthquake excitation so that it is hard to achieve high efficient computation when applying the IS‐FEM to the inelastic response analysis of RC fiber models directly. In this paper, a new numerical scheme for seismic response analysis of RC framed structures model by fiber beam‐column element is proposed based on the IS‐FEM. To implement the RC fiber model for use in IS‐FEM and improve the computational performance of proposed scheme, a method of identifying the local domains with severe section inelasticity level is proposed and a modified Kent‐Park concrete material model is developed. Because the Woodbury formula is adopted as the solver, the global stiffness matrix can keep unchanged throughout the analysis and the main computational effort is only invested on a small matrix representing local inelastic behavior. The numerical examples demonstrate the validity and efficiency of the proposed scheme.

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Section: Inelasticity‐separated Rc Fiber Beam‐column Modelmentioning

confidence: 97%

Section: Background Of Is‐femmentioning

confidence: 99%

Δ d_{in} = Δ d_{in}^{'} + Δ d_{in}^{″},

where

Δ d_{in}^{'}

Δ d_{in}^{″}

is incremental inelastic deformation that is defined as the difference between total section deformation increment Δ d in and the linear‐elastic section deformation increment

Δ d_{in}^{'}

. Thus, the incremental section forces can also be expressed by

([], \begin{array}{c} Δ m_{in} \\ Δ m_{ela} \end{array}) = D_{e} ([], \begin{array}{c} Δ d_{in}^{'} \\ Δ d_{ela} \end{array}) = ([], \begin{array}{c} D_{italicin, e} & bold0 \\ bold0 & D_{ela} \end{array}) ([], \begin{array}{c} Δ d_{in}^{'} \\ Δ d_{ela} \end{array}) = ([], \begin{array}{c} D_{italicin, e} & bold0 \\ bold0 & D_{ela} \end{array}) ((), ([], \begin{array}{c} Δ d_{in} \\ Δ d_{ela} \end{array}) - ([], \begin{array}{c} Δ d_{} \end{array}))

…”

Section: Inelasticity‐separated Rc Fiber Beam‐column Modelmentioning

confidence: 99%

“…For a given element, the principle of virtual work can be expressed by

l \int_{0}^{1} ((), δ d_{in}^{T} normalΔ m_{in} + δ d_{ela}^{T} normalΔ m_{ela}) italicdξ - δ q^{T} normalΔ boldf = 0,

([], \begin{array}{c} boldk & k^{'} \\ {boldk}^{'}^{T} & k_{in}^{″} \end{array}) ([], \begin{array}{c} Δ boldq \\ - Δ {\overset{true¯}{d^{″}}}_{in} \end{array}) = ([], \begin{array}{c} normalΔ boldf \\ bold0 \end{array}),

in which

boldk = l \int_{0}^{1} B^{T} D_{e} boldB italicdξ k^{'} = l \int_{0}^{1} B_{in}^{T} D_{italicin, e} boldC italicdξ k_{in}^{″} = l \int_{0}^{1} C^{T} D_{italicin, e} {({boldD}_{in, e} - {boldD}_{in, t})}^{-}

…”

Section: Inelasticity‐separated Rc Fiber Beam‐column Modelmentioning

confidence: 99%

Section: Section Deformation Decompositionmentioning

confidence: 99%

See 3 more Smart Citations

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

Yu²

2018

Earthq Engng Struct Dyn

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Efficient optimal seismic design method of passive energy dissipation systems based on the inelasticity‐separated finite element method

Luo

et al. 2023

Earthquake Engineering and Resilience

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Installing passive energy dissipation dampers in the main structure is an effective way to reduce structural seismic response. The traditional optimal design of passive energy dissipation systems requires a massive nonlinear time history analysis, which is an extremely inefficient process and, as a result, limits its application in practice. In this paper, an efficient optimal design method for dampers is proposed based on the inelasticity‐separated finite element method (IS‐FEM) and genetic algorithm. The IS‐FEM is a novel efficient structural nonlinear analysis method that can avoid the real‐time updating and decomposition of the structural global stiffness matrix in a traditional structure analysis and only requires a small‐scale Schur complementary matrix representing local nonlinear behavior being decomposed per iteration. To make the IS‐FEM available for the analysis of structures equipped with an energy dissipation system, the inelasticity‐separated governing equations of displacement‐based dampers are derived first. Then, an improved constrained optimal genetic algorithm based on population feasibility is presented to enhance the searching ability near the feasible domain boundary. Finally, an efficient damper optimization design method is proposed by combining the developed genetic algorithm with the proposed IS‐FEM‐based analysis procedure for passive energy dissipation structures. The accuracy and efficiency of the proposed method are verified by designing a set of metallic yield dampers to retrofit a steel structure.

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A Woodbury solution method for efficient seismic collapse analysis of space truss structures based on hybrid nonlinearity separation

2021

Earthq Engng Struct Dyn

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This study presents a fast algorithm for collapse behavior simulation of space truss structures under extreme earthquake excitation by introducing the Woodbury formula to efficiently solve the structural response caused by material and geometric nonlinearity (hybrid nonlinearity). The Woodbury formula, which is an efficient tool in mathematics for solving low-rank perturbation problems, has successfully been used to improve the efficiency of local material nonlinear analysis but still has difficulties with seismic collapse analysis in which geometric nonlinearity should be considered. In this study, by implementing stiffness matrix decomposition according to the unchanged reference configuration, the effects of hybrid nonlinearity on the change in tangent stiffness of truss structures are uniformly formulated in the form of hybrid nonlinear perturbation to the reference elastic stiffness. Thus, a hybrid nonlinearity separated governing equation can be established, in which the hybrid nonlinear behaviors are depicted by the additional nonlinear degrees of freedom (NLDOFs) separated from the reference system. This allows for employing the Woodbury formula to perform seismic collapse analysis of space truss structures for avoiding the repeated updating of the global stiffness. To overcome the adverse effect of the large NLDOF number caused by the global characteristics of geometric nonlinearity on the efficiency advantages of the Woodbury formula during seismic collapse analysis, an element state judgment strategy and an adaptive restart mechanism are presented to activate only a small number of NLDOFs within critical local regions. The accuracy and efficiency of the proposed method are verified by two numerical examples.

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Efficient Inelasticity-Separated Finite-Element Method for Material Nonlinearity Analysis

Cited by 33 publications

References 27 publications

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

Seismic response analysis of reinforced concrete frames using inelasticity‐separated fiber beam‐column model

Efficient optimal seismic design method of passive energy dissipation systems based on the inelasticity‐separated finite element method

A Woodbury solution method for efficient seismic collapse analysis of space truss structures based on hybrid nonlinearity separation

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