Preconditioned Conjugate Gradient Method for Static Reanalysis with Modifications of Supports

Liu, H. F.; Wu, Baisheng; Li, Z. G.

doi:10.1061/(asce)em.1943-7889.0000832

Cited by 15 publications

(4 citation statements)

References 31 publications

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“…The holy grail of mechanical and design reanalysis is to (approx) determine the reaction of structure (stresses, displacements, strains, forces and so on) after some significant modification using the structure's earlier answer, such that, without resolving the rising model equations. During the optimization procedure, the high-fidelity model should be addressed on time, even for a few cycles (Liu et al, 2015). The basis of approximation reanalysis is repeating the Cholesky factorization (Liu et al, 2014) in a series of subsequent iterations (direct solution) usually dependent on predetermined error criterion; Krylov subdomain technique (Herrero-P erez and Mart ınez Castej on, 2021) for iterative solutions.…”

Section: Approximate Reanalysis and Reduced Modelingmentioning

confidence: 99%

Section: Innovation In Optimization Phenomenonmentioning

confidence: 99%

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A review on developing optimization techniques in civil engineering

Zaheer

Manzoor²,

Ahamad³

2023

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PurposeThe purpose of this article is to analyze the optimization process in depth, elaborating on the components of the entire process and the techniques used. Researchers have been drawn to the expanding trend of optimization since the turn of the century. The rate of research can be used to measure the progress and increase of this optimization procedure. This study is phenomenal to understand the optimization process and different algorithms in addition to their application by keeping in mind the current computational power that has increased the implementation for several engineering applications.Design/methodology/approachTwo-dimensional analysis has been carried out for the optimization process and its approaches to addressing optimization problems, i.e. computational power has increased the implementation. The first section focuses on a thorough examination of the optimization process, its objectives and the development of processes. Second, techniques of the optimization process have been evaluated, as well as some new ones that have emerged to overcome the above-mentioned problems.FindingsThis paper provided detailed knowledge of optimization, several approaches and their applications in civil engineering, i.e. structural, geotechnical, hydraulic, transportation and many more. This research provided tremendous emerging techniques, where the lack of exploratory studies is to be approached soon.Originality/valueOptimization processes have been studied for a very long time, in engineering, but the current computational power has increased the implementation for several engineering applications. Besides that, different techniques and their prediction modes often require high computational strength, such parameters can be mitigated with the use of different techniques to reduce computational cost and increase accuracy.

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Section: Approximate Reanalysis and Reduced Modelingmentioning

confidence: 99%

Section: Innovation In Optimization Phenomenonmentioning

confidence: 99%

A review on developing optimization techniques in civil engineering

Zaheer

Manzoor²,

Ahamad³

2023

View full text Add to dashboard Cite

show abstract

“…[1] and references therein). The use of preconditioned conjugate gradients has been exploited in the solution of the linear systems associated with the equilibrium equations [4,5,23,24]. Meshless-based local reanalysis [12] and a meshfree reduced basis approach for large deformations [26] have been analyzed as well.…”

Section: Introductionmentioning

confidence: 99%

Inexact Newton combined approximations in the topology optimization of geometrically nonlinear elastic structures and compliant mechanisms

Senne¹,

Gomes²,

Santos³

2021

Preprint

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This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a sequential piecewise linear programming (SPLP) algorithm. Five distinct strategies have been proposed to control the frequency of the factorizations of the Jacobian matrices of the nonlinear equilibrium equations. Aiming at speeding up the overall iterative scheme while keeping the accuracy of the approximate solutions, three of the strategies also use an ICA scheme for the adjoint linear system associated with the sensitivity analysis. The robustness of the proposed reanalysis strategies is corroborated by means of numerical experiments with four benchmark problems -two structures and two compliant mechanisms. Besides assessing the performance of the strategies considering a fixed budget of iterations, the impact of a theoretically supported stopping criterion for the SPLP algorithm was analyzed as well.

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“…What is more, only self‐similar delamination growth can satisfactorily be dealt with. To overcome the limitations mentioned earlier, some researchers combined a fatigue damage evolution law with the CZM to take both damage initiation and propagation stages into account. Harper and Hallett used a cohesive zone interface element for analyzing the delamination crack propagation under a cyclic load.…”

Section: Introductionmentioning

confidence: 99%

Predicting fatigue damage in interphase of short fiber reinforced rubber composites under transverse load

Chen

2016

Polymer Composites

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A computational model has been established for analyzing the interphase damage of short fiber reinforced rubber composites (SFRCs) under transverse static and fatigue tensile loads. A cohesive zone model was integrated with a stress-based fatigue damage model to simulate the damage initiation and propagation. To obtain the damage model parameters and validate the methodology, some tests of SFRCs under static and fatigue tensile loads were conducted. The simulation results agree well with the experimental data. It is observed that under static loads, the damage of SFRCs is dominated by the interphase damage before the strain reaches 38.04%. Under fatigue loads, the speed of damage propagation increases exponentially with cyclic numbers. Once the crack in the interphase is initiated, it extends to almost the entire interphase after several cycles because of the stress concentration near the crack tip. It is found that a good initial adhesion status of the interphase can effectively improve the antifatigue performance of SFRCs.

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Preconditioned Conjugate Gradient Method for Static Reanalysis with Modifications of Supports

Cited by 15 publications

References 31 publications

A review on developing optimization techniques in civil engineering

A review on developing optimization techniques in civil engineering

Inexact Newton combined approximations in the topology optimization of geometrically nonlinear elastic structures and compliant mechanisms

Predicting fatigue damage in interphase of short fiber reinforced rubber composites under transverse load

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