A modified Lemke Algorithm for dynamic rigid plastic response of skeletal structures

Khan, Azam; Ahmad, Irshad; Khan, W. A.; Khan, Niaz Bahadur; Aslam, Muhammad Shahzad

doi:10.1016/j.compstruc.2021.106638

Cited by 5 publications

(23 citation statements)

References 30 publications

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“…Quadratic programming is a useful computational device ideal for representing discretely rigid-plastic skeletal structures under impulsive loading 22 – 25 . An application of this formulation to layout optimization of impulsively loaded rigid plastic structures is presented by Kaliszky and Logo 26 .…”

Section: Introductionmentioning

confidence: 99%

“…A detailed 1D rigid-plastic modeling strategy has been developed previously 25 , 30 which was validated against the continuum solution of the impacted beam. This numerical approach, formulated as a Linear Complementarity Problem (LCP), led to fast and accurate dynamic response prediction, unlike the commercial finite element softwares that require extensive computer memory and a longer execution time 60 .…”

Section: Introductionmentioning

confidence: 99%

“…This numerical approach, formulated as a Linear Complementarity Problem (LCP), led to fast and accurate dynamic response prediction, unlike the commercial finite element softwares that require extensive computer memory and a longer execution time 60 . However, there were instances when the accuracy of the LCP solver 25 was undermined by issues concerning numerical instability. These problems were attributed to the approximate initial velocity profile, which is required to initiate the numerical process.…”

Section: Introductionmentioning

confidence: 99%

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Flexure and shear response of an impulsively loaded rigid-plastic beam by enhanced linear complementarity approach

Khan

Tariq

Ullah

et al. 2022

Sci Rep

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The linear complementarity approach has been utilized as a systematic and unified numerical process for determining the response of a rigid-plastic structure subjected to impulsive loading. However, the popular Lemke Algorithm for solving linear complementarity problems (LCP) encounters numerical instability issues whilst tracing the response of structures under extreme dynamic loading. This paper presents an efficient LCP approach with an enhanced initiation subroutine for resolving the numerical difficulties of the solver. The numerical response of the impulsively loaded structures is affected by the initial velocity profile, which if not found correctly can undermine the overall response. In the current study, the initial velocity profile is determined by a Linear Programming (LP) subroutine minimizing the energy function. An example of a uniform impulsively loaded simply supported beam is adduced to show the validity and accuracy of the proposed approach. The beam is approximated with bending hinges having infinite resistance to shear. Comparison of the numerical results to the available closed-form solution confirms the excellent performance of the approach. However, a subsequent investigation into a beam having the same support conditions and the applied loading, but with bending and shear deformation, results in numerical instability despite optimizing the initial velocity profile. Thus a more generic description of kinetics and kinematics is proposed that can further enhance the numerical efficiency of the LCP formulation. The ensuing numerical results are compared with the available close form solution to assess the accuracy and efficiency of the developed approach.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Flexure and shear response of an impulsively loaded rigid-plastic beam by enhanced linear complementarity approach

Khan

Tariq

Ullah

et al. 2022

Sci Rep

Self Cite

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show abstract

“…In that study, the LCP solution was employed as a simplified design procedure for the assessment of structures under impact loading. This type of loading required an initial velocity profile for starting the Lemke Algorithm (Khan et al, 2021). However, it was shown (Khan et al, 2013) that such problems posed considerable numerical difficulties in finding solutions for simple bending-only models.…”

Section: Introductionmentioning

confidence: 99%

“…These numerical problems were avoided by considering the bending-shear interaction in the model. In a recent research (Khan et al, 2021), the Lemke algorithmic solution was tested by investigating several engineering problems; these included a simply supported beam subjected to rectangular pulse load and a portal frame subjected to triangular pulse load. A comparison of the LCP approach with the theoretical and the numerical solutions using lumped mass discretization showed excellent agreement.…”

Section: Introductionmentioning

confidence: 99%

An Improved Linear Complementarity Solver for the Dynamic Analysis of Blast Loaded Structures

Khan

Tariq

Ullah

et al. 2022

Int J Concr Struct Mater

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The linear complementarity problem (LCP) approach, expedited by using the simple rigid–plastic theory, has been utilized successfully in predicting the numerical response of the ductile steel or concrete structures subjected to short-duration, high-intensity dynamic loads. The current study attempts to improve the computational stability of this powerful technique while determining the response of skeletal structures under blast loading. The performance of the Lemke LCP solver is amplified by introducing an automatic time-stepping scheme to efficiently trace the complex dynamic response using either lumped mass or continuous mass discretization. The computational efficiency of this solver is tested against carefully chosen three numerical examples, and the acquired results are in good agreement with the derived closed-form solution and results from other sources.

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A Time-Step-Modified Linear Complementarity Approach for Analysing a Simply Supported Steel Beams Subjected to Far-Field Blast Loading

Tariq,

Khan,

Khan

et al. 2024

Int J Steel Struct

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A modified Lemke Algorithm for dynamic rigid plastic response of skeletal structures

Cited by 5 publications

References 30 publications

Flexure and shear response of an impulsively loaded rigid-plastic beam by enhanced linear complementarity approach

Flexure and shear response of an impulsively loaded rigid-plastic beam by enhanced linear complementarity approach

An Improved Linear Complementarity Solver for the Dynamic Analysis of Blast Loaded Structures

A Time-Step-Modified Linear Complementarity Approach for Analysing a Simply Supported Steel Beams Subjected to Far-Field Blast Loading

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