Abstract
This article presents an extended algorithm for topology optimization of compliant mechanisms and structures with design-dependent pressure loadings using the moving iso-surface threshold (MIST) method. In this algorithm, the fluid-structure interface is modeled using the finite element method via considering equivalent virtual strain energy and work and is tracked by an element-based searching scheme. Design-dependent pressure loads are directly applied on interface boundary and are calculated as virtual work equivalent nodal forces in the interface elements based on the finite element formulation. Several numerical examples are presented for topology optimization of mean compliance and compliant mechanisms. The present algorithm is validated through benchmarking with the results in literature and/or full finite element analysis (FEA) results of the optimum compliant mechanism and structure designs.
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Abbreviations
- σ :
-
Stress vector
- ε :
-
Strain vector
- u :
-
Displacement
- F :
-
Force vector
- f p :
-
Pressure load vector
- f b :
-
Body force vector
- Ω:
-
Design domain
- Γ:
-
Topology boundary
- V :
-
Total volume
- V f :
-
Volume fraction
- x e :
-
Solid material area ratio for element e
- x e :
-
Vector of xe for all elements
- D :
-
Constitutive matrix
- B :
-
Strain-displacement matrix
- N :
-
Shape function matrix
- p :
-
Material penalty factor
- ζ:
-
Local coordinate along interface boundary
- ξ, η:
-
Element natural coordinates
- J :
-
Objective function
- Φ:
-
Physical response function
- t :
-
Threshold level
- H :
-
Heaviside function
- k Φ, α :
-
Coefficients for constructing Φ
- k mv :
-
Move limit
- P:
-
Pressure magnitude
- k :
-
Spring stiffness
- E :
-
Young’s modulus
- υ :
-
Poisson’s ratio
- e :
-
Element e
- i :
-
Subdomain/element node number
- min:
-
Minimum value
- solid:
-
Solid material
- out:
-
Output degree of freedom
- sed:
-
Strain energy density
- med:
-
Mutual strain energy density
- (1), (2):
-
Real and virtual load cases
- k :
-
Iteration numbering
- (1), (2):
-
Real and virtual load cases
- 1pt :
-
1-point Gaussian quadrature
- ex :
-
Exact integration
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Acknowledgments
Y.L. is a recipient of the Engineering and Information Technologies Research Scholarship from the University of Sydney and we are grateful for the support from the University of Sydney. L.T. would like to acknowledge the support of the Australian Research Council (Grant Number: DP140104408, DP170104916).
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Lu, Y., Tong, L. Topology optimization of compliant mechanisms and structures subjected to design-dependent pressure loadings. Struct Multidisc Optim 63, 1889–1906 (2021). https://doi.org/10.1007/s00158-020-02786-y
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DOI: https://doi.org/10.1007/s00158-020-02786-y