New three-dimensional time-stepping transient fundamental solutions with applications

Article Engineering, Mechanical

Time-Differencing Fundamental Solutions for Plane Elastodynamics

Ahmed Fady Farid et al.

Summary: New fundamental solutions for dynamic analysis of plane elastodynamics are developed in this paper. The governing dynamic differential equations are rewritten by replacing the accelerations with the corresponding displacements at different time steps via a suitable finite difference scheme, enhancing the accuracy of the solutions.

JOURNAL OF ENGINEERING MECHANICS (2022)

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Article Engineering, Chemical

An accurate numerical method for inversion of Laplace transforms with applications in process dynamics and control

Hooman Fatoorehchi

Summary: In this paper, a novel numerical method for inverting Laplace transforms is developed, with proven efficiency and reliability through numerical simulations. The method is highly accurate and requires the Laplace transform function to only be defined on the real axis.

CANADIAN JOURNAL OF CHEMICAL ENGINEERING (2021)

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Article Computer Science, Interdisciplinary Applications

BESLE: Boundary element software for 3D linear elasticity

Andres F. Galvis et al.

Summary: BESLE is an open-source code for analyzing the mechanical behavior of heterogeneous materials using the boundary element method in 3D with both elastostatic and elastodynamic capabilities. It can simulate isotropic and anisotropic materials comprised of single or multiple domains, with results described by displacement and traction fields, as well as stress and strain tensors available for post-processing. The software is implemented in Fortran-MPI and is best suited for multi-core architectures for efficient parallelization.

COMPUTER PHYSICS COMMUNICATIONS (2021)

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Article Computer Science, Artificial Intelligence

Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Yuan Li et al.

Summary: This paper proposes using partially discontinuous elements to improve the computation of 3D elastodynamics, by shrinking corner nodes into elements to reduce the impact of node positions on results and generating a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces. The numerical integration scheme and element subdivision method are presented to enhance accuracy and stability, with the effectiveness of the proposed method verified through numerical examples. Case studies on the influence of node positions on computation results are conducted, and a recommended range of inward shrink ratio for element nodes is provided.

ALGORITHMS (2021)

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Article Engineering, Multidisciplinary