journal article·2023-08-14Open access

Assessing the Structural Performance of Biodegradable Capsules

Harri Hakula

Applied Sciences· Volume 13· Issue 16

Abstract

Biodegradable materials pose challenges over all aspects of computational mechanics. In this study, the focus is on the resulting domain uncertainty. Model structures or devices are shells of revolution subject to random variation of the outer surface. The novelty of the proposed computational approach is the possibility to restrict the variation to specific parts of the structure using a posteriori filtering, which is applied to the random process whose realisations are the profiles of the shells. The dimensionally reduced stochastic elasticity problems are solved using a collocation method where every realisation is discretised separately. The collocation scheme is validated against standard Monte Carlo. The reliability of the simulations is further confirmed via a posteriori error estimates that are computed using the same collocation scheme. The quantities of interest on the nominal domain are the expected displacement fields and their variances.
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Research context

OpenAlex topics: Probabilistic and Robust Engineering Design · Asphalt Pavement Performance Evaluation · Concrete Corrosion and Durability

SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.

Affiliations

Department of Mathematics and Systems Analysis, Aalto University, Otakaari 1, 00076 Aalto, Finland

References (29)

Show source-provided references
1. Structural analysis, and antioxidant and antibacterial properties of chitosan-poly (vinyl alcohol) biodegradable films10.1007/s11356-016-6699-9 ↗
2. Basic mechanical analysis of biodegradable materials10.1088/1757-899X/968/1/012010 ↗
3. Pires, J.R.A., Souza, V.G.L., Fuciños, P., Pastrana, L., and Fernando, A.L. (2022). Methodologies to Assess the Biodegradability of Bio-Based Polymers – Current Knowledge and Existing Gaps. Polymers, 14.10.3390/polym14071359 ↗
4. Modulating sustained drug release from nanocellulose hydrogel by adjusting the inner geometry of implantable capsules10.1016/j.jddst.2020.101625 ↗
5. Optimality of adaptive Galerkin methods for random parabolic partial differential equations10.1016/j.cam.2013.12.031 ↗
6. Stochastic Static Analysis of Planar Elastic Structures with Multiple Spatially Uncertain Material Parameters10.3390/applmech3030055 ↗
7. Vries, J.D. (2009). The Imperfection Data Bank and Its Applications. [Ph.D. Thesis, TU Delft].
8. On solving elliptic stochastic partial differential equations10.1016/S0045-7825(02)00354-7 ↗
9. On output functionals of boundary value problems on stochastic domains
10. Sparse second moment analysis for elliptic problems in stochastic domains10.1007/s00211-008-0147-9 ↗
11. Stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains10.1002/nme.3004 ↗
12. Numerical methods for differential equations in random domains10.1137/040613160 ↗
13. Szabo, B., and Babuška, I. (1991). Finite Element Analysis, Wiley.
14. Hakula, H., Harbrecht, H., Kaarnioja, V., Kuo, F.Y., and Sloan, I.H. (2023, July 01). Uncertainty Quantification for Random Domains Using Periodic Random Variables, Available online: http://xxx.lanl.gov/abs/2210.17329.
15. Conjugate Function Method for Numerical Conformal Mappings10.1016/j.cam.2012.06.003 ↗
16. Spectral discretization errors in filtered subspace iteration10.1090/mcom/3483 ↗
17. An h-p-n adaptive finite element scheme for shell problems10.1016/0965-9978(95)00126-3 ↗
18. The p- and h-p versions of the finite element method, an overview10.1016/0045-7825(90)90011-A ↗
19. Schwab, C. (1998). p- and hp-Finite Element Methods, Oxford University Press.
20. Transfinite element methods: Blending function interpolation over arbitrary curved element domains10.1007/BF01436298 ↗
21. Stochastic Galerkin approximation of the Reynolds equation with irregular film thickness10.1016/j.camwa.2017.06.012 ↗
22. Schenk, C.A., and Schuëller, G.I. (2005). Uncertainty Assessment of Large Finite Element Systems, Springer. Lecture Notes in Applied and Computational Mathematics.10.1007/11673941_11 ↗
23. Ghanem, R., and Spanos, P. (2003). Stochastic Finite Elements: A Spectral Approach, Dover Publications, Inc.
24. Karhunen-Loève approximation of random fields by generalized fast multipole methods10.1016/j.jcp.2006.01.048 ↗
25. A stochastic collocation method for elliptic partial differential equations with random input data10.1137/050645142 ↗
26. An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data10.1137/070680540 ↗
27. A Sparse Composite Collocation Finite Element Method for Elliptic SPDEs10.1137/090750743 ↗
28. Sparse Tensor Approximation of Parametric Eigenvalue Problems10.1007/978-3-642-22061-6_7 ↗
29. Xiu, D. (2010). Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press.10.1515/9781400835348 ↗