Generalisation of non-iterative methods for the modelling of structures under non-proportional loading

Graça-e-Costa, R.; Alfaiate, J.; Dias-da-Costa, D.; Neto, Pedro; Sluys, L.J.

doi:10.1007/s10704-013-9851-2

Cited by 24 publications

(10 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The beam was previously studied numerically using different methods including non-linear finite element analysis and SLA [17]. The problem was also solved by Graça-e-Costa et al [38] using a pair of incremental-only methods that combined tangents and secant solutions. The crack band width, h, used in these analyses was constant and had a value of 20 mm, the same value used by DeJong et al [17].…”

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

Use of negative stiffness in failure analysis of concrete beams

Al‐Sabah

Laefer

2016

Engineering Structures

View full text Add to dashboard Cite

A new concrete analysis method is presented entitled continuous, incremental-only, tangential analysis (CITA). CITA employs piece-wise linear stress-strain curve and a tangent elasticity modulus to calculate stiffness including parts with negative values. Since indefinite structure stiffness matrices generally indicate instability, traditionally they have been avoided. However, since CITA analysis involves introducing damage in steps, the full range of concrete behaviour including the softening portion under tensile cracking can be addressed. Herein CITA is verified against numerical and experimental results for concrete beams, thereby showing faster solutions for non-linear problems than sequentially-linear analysis, while reducing self-imposed restrictions against negative stiffness.

show abstract

Section: Examplementioning

confidence: 99%

“…The models were loaded by a pair of downward base loads at the beam's third points, each of 1 kN. The adopted material properties in this analysis were the same as those used by DeJong et al [17] and Graça-E-Costa et al [38]. In all three models, the control node was the same as the loaded node.…”

Section: Cita Solution Using 1-d Frame Elementsmentioning

confidence: 99%

Use of negative stiffness in failure analysis of concrete beams

Al‐Sabah

Laefer

2016

Engineering Structures

View full text Add to dashboard Cite

show abstract

“…An energy criterion follows the path leading to the highest dissipation of energy. A comprehensive discussion about this algorithm is found in [25,26].…”

Section: Crack Propagation and Solution Proceduresmentioning

confidence: 99%

Validation of a Discrete Crack Model for Lightweight Aggregate Concrete Beams

Dias-da-Costa¹,

Graça-e-Costa²,

Carmo³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

Self Cite

View full text Add to dashboard Cite

show abstract

“…It has been a proven alternative to traditional incremental‐iterative methods for NLFEA of quasi‐brittle structures. SLA, thus far, has had contributions in the contexts of mesh‐objectivity, saw‐tooth laws for extremely brittle materials with snap‐back at constitutive level like glass, extension to non‐proportional loading situations, stepwise secant Coulomb friction laws, creep‐induced cracking, combined incremental‐total approaches like Non‐Iterative Energy‐based Method (NIEM) and the automatic method, combining SLA with a crack tracking technique and non‐proportional loading strategies for three‐dimensional (3D) stress states.…”

Section: Introductionmentioning

confidence: 99%

“…To address this issue, and efficiently make use of previous stiffness matrix factorisations and solutions, two solution strategies are proposed in this article. Alternative methods combining a traditional incremental‐iterative technique and the total approach of SLA are also available in the literature addressing the need for a practical alternative, but the focus of this work is to solely improve the performance of SLA with regards to solving the system of linear equations.…”

Section: Introductionmentioning

confidence: 99%

Two solution strategies to improve the computational performance of sequentially linear analysis for quasi‐brittle structures

Pari

Swart

Gijzen

et al. 2020

Numerical Meth Engineering

View full text Add to dashboard Cite

Summary Sequentially linear analysis (SLA), an event‐by‐event procedure for finite element (FE) simulation of quasi‐brittle materials, is based on sequentially identifying a critical integration point in the FE model, to reduce its strength and stiffness, and the corresponding critical load multiplier (λcrit), to scale the linear analysis results. In this article, two strategies are proposed to efficiently reuse previous stiffness matrix factorisations and their corresponding solutions in subsequent linear analyses, since the global system of linear equations representing the FE model changes only locally. The first is based on a direct solution method in combination with the Woodbury matrix identity, to compute the inverse of a low‐rank corrected stiffness matrix relatively cheaply. The second is a variation of the traditional incomplete LU preconditioned conjugate gradient method, wherein the preconditioner is the complete factorisation of a previous analysis step's stiffness matrix. For both the approaches, optimal points at which the factorisation is recomputed are determined such that the total analysis time is minimised. Comparison and validation against a traditional parallel direct sparse solver, with regard to a two‐dimensional (2D) and three‐dimensional (3D) benchmark study, illustrates the improved performance of the Woodbury‐based direct solver over its counterparts, especially for large 3D problems.

show abstract

Generalisation of non-iterative methods for the modelling of structures under non-proportional loading

Cited by 24 publications

References 16 publications

Use of negative stiffness in failure analysis of concrete beams

Use of negative stiffness in failure analysis of concrete beams

Validation of a Discrete Crack Model for Lightweight Aggregate Concrete Beams

Two solution strategies to improve the computational performance of sequentially linear analysis for quasi‐brittle structures

Contact Info

Product

Resources

About