A Stochastic Framework for Saint-Venant Torsion in Spherical Shells: Monte Carlo Implementation of the Feynman–Kac Approach
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| izdano v: | Symmetry vol. 17, no. 6 (2025), p. 878-900 |
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| Drugi avtorji: | , , |
| Izdano: |
MDPI AG
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| Teme: | |
| Online dostop: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 045 | 2 | |b d20250101 |b d20251231 | |
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| 100 | 1 | |a Moghaddam, Behrouz Parsa |u Department of Mathematics, La.C., Islamic Azad University, Lahijan P.O. Box 44169-39515, Iran; bparsa@iau.ac.ir | |
| 245 | 1 | |a A Stochastic Framework for Saint-Venant Torsion in Spherical Shells: Monte Carlo Implementation of the Feynman–Kac Approach | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a This research introduces an innovative probabilistic method for examining torsional stress behavior in spherical shell structures through Monte Carlo simulation techniques. The spherical geometry of these components creates distinctive computational difficulties for conventional analytical and deterministic numerical approaches when solving torsion-related problems. The authors develop a comprehensive mesh-free Monte Carlo framework built upon the Feynman–Kac formula, which maintains the geometric symmetry of the domain while offering a probabilistic solution representation via stochastic processes on spherical surfaces. The technique models Brownian motion paths on spherical surfaces using the Euler–Maruyama numerical scheme, converting the Saint-Venant torsion equation into a problem of stochastic integration. The computational implementation utilizes the Fibonacci sphere technique for achieving uniform point placement, employs adaptive time-stepping strategies to address pole singularities, and incorporates efficient algorithms for boundary identification. This symmetry-maintaining approach circumvents the mesh generation complications inherent in finite element and finite difference techniques, which typically compromise the problem’s natural symmetry, while delivering comparable precision. Performance evaluations reveal nearly linear parallel computational scaling across up to eight processing cores with efficiency rates above 70%, making the method well-suited for multi-core computational platforms. The approach demonstrates particular effectiveness in analyzing torsional stress patterns in thin-walled spherical components under both symmetric and asymmetric boundary scenarios, where traditional grid-based methods encounter discretization and convergence difficulties. The findings offer valuable practical recommendations for material specification and structural design enhancement, especially relevant for pressure vessel and dome structure applications experiencing torsional loads. However, the probabilistic characteristics of the method create statistical uncertainty that requires cautious result interpretation, and computational expenses may surpass those of deterministic approaches for less complex geometries. Engineering analysis of the outcomes provides actionable recommendations for optimizing material utilization and maintaining structural reliability under torsional loading conditions. | |
| 653 | |a Finite element method | ||
| 653 | |a Accuracy | ||
| 653 | |a Torsional stress | ||
| 653 | |a Performance evaluation | ||
| 653 | |a Brownian motion | ||
| 653 | |a Pressure vessels | ||
| 653 | |a Finite difference method | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Structural design | ||
| 653 | |a Statistical analysis | ||
| 653 | |a Boundary conditions | ||
| 653 | |a Symmetry | ||
| 653 | |a Efficiency | ||
| 653 | |a Machine learning | ||
| 653 | |a Stochastic processes | ||
| 653 | |a Spherical shells | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Coordinate transformations | ||
| 653 | |a Fourier transforms | ||
| 653 | |a Probabilistic methods | ||
| 653 | |a Monte Carlo simulation | ||
| 653 | |a Probability theory | ||
| 653 | |a Stochastic models | ||
| 653 | |a Algorithms | ||
| 653 | |a Structural reliability | ||
| 653 | |a Mesh generation | ||
| 700 | 1 | |a Zaky, Mahmoud A |u Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11566, Saudi Arabia; mibrahimm@imamu.edu.sa | |
| 700 | 1 | |a Sedaghat Alireza |u Department of Mechanical Engineering, La.C., Islamic Azad University, Lahijan P.O. Box 44169-39515, Iran; sedaghat.alirezaa@iau.ac.ir | |
| 700 | 1 | |a Galhano Alexandra |u Faculdade de Ciências Naturais, Engenharias e Tecnologias, Universidade Lusófona—CUP, Rua Augusto Rosa 24, 4000-098 Porto, Portugal | |
| 773 | 0 | |t Symmetry |g vol. 17, no. 6 (2025), p. 878-900 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3223942472/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3223942472/fulltextwithgraphics/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3223942472/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |