Elastoplastic Analysis of Plates with Radial Point Interpolation Meshless Methods
Abstract
:1. Introduction
2. Meshless Methods
2.1. The Radial Point Interpolation Method
2.2. Discrete System of Equations
3. Elastoplastic Analysis
- a yield criterion, indicating the stress level at which plastic flow initiates, and an initial yield surface, defining the elastic limit in a multiaxial stress state;
- a hardening law, describing the evolution of the subsequent yield surfaces; and
- a flow rule, relating the plastic deformation to the current stresses in the material and the stress increments outside the yield surface.
3.1. Elastoplastic Constitutive Model
3.2. Stress-Returning Algorithm
3.3. Nonlinear Solution Algorithm
- 1.
- Set the incremental load, .
- 2.
- Loop over all integration points, .
- 3.
- Assemble the global tangent stiffness matrix: .
- 4.
- Solve .
- 5.
- Update the displacement field: .
- 6.
- Loop over all integration points, .
- (a)
- Evaluate the strain increment: .
- (b)
- Considering the elastic constitutive matrix, Equation (46), obtain the incremental stress state: .
- (c)
- Calculate the trial stress state: .
- (d)
- Verify if: . If so, . Otherwise, the algorithm presented in Section 3.2 is applied, which will lead to .
- (e)
- Update the stress field: .
- 7.
- Calculate the residual force vector: .
- 8.
- Apply a residual force convergence criteria: .
- (a)
- if , being a small threshold value (such as ), then, the process moves to point 2, initialising a new increment: , and assuming a new force increment: .
- (b)
- If , then the iterative process begins, attempting to achieve . Thus, the process moves to point 2, initialising iteration j, assuming a new force increment: .
4. Numerical Results
4.1. Normalized Central Displacement
4.2. Stress Diagrams through the Plate’s Thickness
4.3. Effective Stress Maps
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
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Belinha, J.; Aires, M. Elastoplastic Analysis of Plates with Radial Point Interpolation Meshless Methods. Appl. Sci. 2022, 12, 12842. https://doi.org/10.3390/app122412842
Belinha J, Aires M. Elastoplastic Analysis of Plates with Radial Point Interpolation Meshless Methods. Applied Sciences. 2022; 12(24):12842. https://doi.org/10.3390/app122412842
Chicago/Turabian StyleBelinha, Jorge, and Miguel Aires. 2022. "Elastoplastic Analysis of Plates with Radial Point Interpolation Meshless Methods" Applied Sciences 12, no. 24: 12842. https://doi.org/10.3390/app122412842
APA StyleBelinha, J., & Aires, M. (2022). Elastoplastic Analysis of Plates with Radial Point Interpolation Meshless Methods. Applied Sciences, 12(24), 12842. https://doi.org/10.3390/app122412842