Structural Engineering and Mechanics

Techno-Press (테크노프레스)
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A computationally efficient numerical integration scheme for non-linear plane-stress/strain FEM applications using one-point constitutive model evaluation

  • Hector R., Amezcua (Institute of Engineering, National Autonomous University of Mexico, UNAM) ;
  • Amado G., Ayala (Institute of Engineering, National Autonomous University of Mexico, UNAM)
  • Received : 2022.08.04
  • Accepted : 2022.12.14
  • Published : 2023.01.10
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Abstract

This work presents a proposal for employing reduced numerical integration in the formulation of the 4-node quadrilateral solid finite element. The use of these low-order integration rules leads to numerical instabilities such as those producing the hourglass effect. The proposed procedure allows evaluating a given constitutive model only in one integration point, achieving an attractive computational cost reduction and, also, successfully controls the hourglass effect. A validation of the proposal is included and discussed throughout the paper. To show the efficiency of the proposal, several application examples of masonry structures are studied and discussed. To represent the non-linear mechanical behaviour of masonry a plastic-damage model is implemented within the application of this sub-integration scheme. Also, in order to have a full and computationally efficient strategy to determine the behaviour of masonry structures, involving its evolution to collapse, a homogenization technique with a macro-modeling approach is used. The methodology discussed throughout this paper demonstrates a substantial computational cost reduction and an improved approximation of the non-linear problem evidenced by a reduction of up to 85% of the computational time for some cases.

Keywords

Acknowledgement

This research was supported by the General Directorate for Affairs of Academic Personnel (DGAPA) of the National Autonomous University of Mexico, through the PAPIIT project number IN106917. Additionally, the first author greatly appreciates the graduate scholarship provided by the National Council for Science and Technology (CONACYT). Finally, the authors thank the meaningful contributions of Dr. Juan Gutierrez.

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