A robust continuation method to pass limit-point instability

Jorabchi, Kavous; Suresh, Krishnan

doi:10.1016/j.finel.2011.05.012

Cited by 5 publications

(3 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From dynamical point of view, a limit point splits the homotopy path into stable and unstable portions [38], signifying a change in the dynamical stability. When κ is decreasing, the dynamics are unstable and the homotopy path cannot reach the solution [39].…”

Section: A Two-layer Path Tracking Methodsmentioning

confidence: 99%

A Homotopy Method Based on Theory of Functional Connections

Wang,

Topputo

2019

Preprint

View full text Add to dashboard Cite

Discrete continuation method (DCM) is a widely used homotopy method to solve optimal control problems. Starting from auxiliary problem, DCM monotonously varies homotopy parameter until the objective problem is solved. However, DCM often fails when the initially and manually defined homotopy path exists limit points or goes off to infinity. In this paper, a novel homotopy method, called TFC homotopy method, is presented to enhance DCM performance in aspect of homotopy function construction. Firstly, Theory of Functional Connections (TFC) is introduced and TFC homotopy function is established, which implicitly defines infinite homotopy paths that connect the auxiliary problem with the objective problem for the first time in literature. Secondly, a novel two-layer path tracking method is designed. DCM is used in the first layer and the second layer is triggered when unfavorable situations are met, then another feasible homotopy path is found by solving an optimization problem and tracked by DCM. Compared with pseudo-arclength method (PAM), TFC homotopy method remains the simplicity of DCM method while owing its capability of flexible path switching. Multiple simulations are conducted against PAM, illustrating the effectiveness of the proposed method.

show abstract

Section: A Two-layer Path Tracking Methodsmentioning

confidence: 99%

A Homotopy Method Based on Theory of Functional Connections

Wang,

Topputo

2019

Preprint

View full text Add to dashboard Cite

show abstract

“…For a more detailed explanation of the method, the reader is referred to the works by He [31][32][33][34]. Several authors have expanded upon this method to create new iteration schemes [35], or pass load limit points in nonlinear geometric analysis [36], for example. The method has also been used for various applications including nonlinear wave equations [37][38][39], nonlinear heat transfer [40][41][42], and calculating Adomian polynomials [43][44][45], to name a few.…”

Section: Related Workmentioning

confidence: 99%

A Unified Library of Nonlinear Solution Schemes

Leon

Paulino

Pereira

et al. 2011

Applied Mechanics Reviews

View full text Add to dashboard Cite

Nonlinear problems are prevalent in structural and continuum mechanics, and there is high demand for computational tools to solve these problems. Despite efforts to develop efficient and effective algorithms, one single algorithm may not be capable of solving any and all nonlinear problems. A brief review of recent nonlinear solution techniques is first presented. Emphasis, however, is placed on the review of load, displacement, arc length, work, generalized displacement, and orthogonal residual control algorithms, which are unified into a single framework. Each of these solution schemes differs in the use of a constraint equation for the incremental-iterative procedure. The governing finite element equations and constraint equation for each solution scheme are combined into a single matrix equation, which characterizes the unified approach. This conceptual model leads naturally to an effective object-oriented implementation. Within the unified framework, the strengths and weaknesses of the various solution schemes are examined through numerical examples. [DOI: 10.1115/1.4006992]

show abstract

“…Therefore, an appropriate approach is the usage of a non-linear structural analysis method for the computation of the member and joint responses. [5][6][7][8]. Following the computation of member responses, the capacities of member strengths is checked according to an available national or international design code [9].…”

Section: Introductionmentioning

confidence: 99%

Design Optimization of Lattice Girders According to Member and Joint-Related Design Constraints

2021

View full text Add to dashboard Cite

This study concerns with the design optimization of geometrically nonlinear lattice girders. The novelty of this study comes from simultaneously using the member and joint related design constraints, which are borrowed from the provisions of API RP2A-LRFD specification and defined depending on both member and joint strengths. A multi-objective design optimization approach named ImpNSGAII, which was improved in way of integrating both a neural network implementation and an automatic generating lattice girder tool for the search mechanism of NSGAII, is utilized in this study. Hence, this study purposes to investigate how to vary the optimality quality depending on the presence of joint strength-related design constraints. Thus, it is demonstrated that the presence of the joint strengthrelated design constraints causes to a divergence in the construction cost of optimal designs. Consequently, it is proved that the ImpNSGAII has a higher capability of exploring a conceptual lattice girder configuration in order to obtain an optimal design satisfying the economy, load-resistance and serviceability-related design conditions at the same time.

show abstract

A robust continuation method to pass limit-point instability

Cited by 5 publications

References 39 publications

A Homotopy Method Based on Theory of Functional Connections

A Homotopy Method Based on Theory of Functional Connections

A Unified Library of Nonlinear Solution Schemes

Design Optimization of Lattice Girders According to Member and Joint-Related Design Constraints

Contact Info

Product

Resources

About