Investigation of rigid-plastic beams subjected to impact using linear complementarity

Khan, Azam; Smith, David L.; Izzuddin, B.A.

doi:10.1016/j.engstruct.2012.12.005

Cited by 14 publications

(31 citation statements)

References 29 publications

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“…In the previous research 30 , the formulation in the form of a Linear Complementarity Problem (LCP) has been developed to determine the response of rigid-plastic beams under impact loading. The initiation sub-routine of that formulation is modified herein to resolve the numerical difficulties that appeared previously.…”

Section: Improved Dynamic Rigid-plastic Modelmentioning

confidence: 99%

“…A further extension of the quadratic program has been rigid plastic modeling of walls subjected to extreme dynamic loading 27 . Essentially, the concept of mathematical programming has been successfully employed by Smith and Sahlit 28 , 29 and Khan et al 30 .…”

Section: Introductionmentioning

confidence: 99%

“…Mathematical convenience has motivated researchers to approximate the interaction relation to rectangular yield criterion, Symonds 48 , 49 , 54 . This approach has lead to the notion of shear sliding within the sheared zone is commonly adopted 50 , 52 , 55 – 59 , which can be conveniently modeled by 1D rigid-plastic solid elements 30 .…”

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%

“…Lumped mass and continuous mass elements are employed to model simply supported beam having infinite resistance to shear deformation. The beam is subjected to impulsive loading and the initial velocity profile is determined from the newly developed LP, which is implemented in the LCP approach 30 . The accuracy and numerical efficiency of the results are confirmed by comparing the results with the continuum solution of the beam problem.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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: Improved Dynamic Rigid-plastic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%