Novel Quadrature-Element Analysis of Plane Stress Elastoplasticity
Publication: Journal of Engineering Mechanics
Volume 149, Issue 8
Abstract
A novel quadrature element for performing plane stress elastoplastic analysis is introduced in this paper. Differing from the popular finite-element method, the quadrature-element method (QEM) first evaluates the integration in the weak-form statement of the problem by an integral quadrature scheme, and then approximates the differentiation at the discrete integration points by the differential quadrature analog. As a result, the QEM avoids construction of shape functions and obtains higher-order elements easily by just increasing the order of integration. The usage of higher-order elements leads to more accurate solutions and coarser geometric meshes without detriment to the computational scale because the number of degrees of freedom is maintained. In addition, the element nodes in the QEM are the same as the integration points that possess physical meanings such as strains and stresses, which is crucial in the elastoplastic analysis for determining the elastic/plastic state of the nodes. A straightforward elastoplastic quadrature-element formulation is developed. Incremental-iterative and return mapping solution schemes are adopted to implement the quadrature element for the elastoplastic analysis. Numerical examples are presented to demonstrate the effectiveness and high accuracy of the proposed approach.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 8 • August 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Nov 13, 2022
Accepted: Mar 25, 2023
Published online: May 24, 2023
Published in print: Aug 1, 2023
Discussion open until: Oct 24, 2023
ASCE Technical Topics:
- Analogs
- Construction engineering
- Construction management
- Continuum mechanics
- Deformation (mechanics)
- Elastic analysis
- Elastoplasticity
- Engineering fundamentals
- Engineering mechanics
- Finite element method
- Geomatics
- Integrals
- Mapping
- Mathematics
- Methodology (by type)
- Numerical methods
- Solid mechanics
- Stress (by type)
- Stress analysis
- Structural analysis
- Structural engineering
- Structural mechanics
- Surveying methods
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