Aug 2026· Mathematical methods in the applied sciences· 0 citations· 22 references
Abstract
This paper focuses on optimal design problems in the context of the Kirchhoff‐Love model for pure bending of a thin, solid, symmetric plate under a transverse load. The objective is to simultaneously determine the optimal outer shape of the domain and the distribution of two isotropic materials within the domain in order to minimize compliance. The proposed optimization strategy integrates homogenization techniques with shape optimization. The level‐set function is utilized to propagate the movement of the outer boundary through a calculated shape derivative, while the interior is optimized using a known optimality criteria method for the single‐state compliance minimization problem. A numerical scheme implementing this coupled approach is presented and validated through several examples. Finally, the proposed method is compared with the pure homogenization and the pure shape optimization method and is shown to yield improved performance.
The optimum shape design algorithm presented formulates the shape optimization problem by treating the nodal coordinates of thin-walled sections. The displacement, normal, and shear stress limitations are considered design constraints, while the objective function minimizes weight. The effect of warping is considered i...
Background/Aim: This study develops and verifies a finite-difference formulation for the linear buckling analysis of rectangular power-law functionally graded material (P-FGM) plates, based on first-order shear deformation theory (FSDT). The aim is to provide an accurate, computationally efficient numerical approach fo...
Khaled Benmahdi, Ali Meksi, Mohamed Sadoun et al.· Vojnotehnički Glasnik· 0 citations
In this paper, we use a mixed boundary-value problem to describe the deflection of a plate under longitudinal and transverse loading located on an elastic basis, with the mandatory presence of a Dirichlet boundary condition. We fictitiously continue the boundary-value problem across the boundary with a Dirichlet condit...
S. I. Ebel, A. Ushakov· Izvestiya Vysshikh Uchebnykh...· 0 citations
To address the configuration optimisation and interface representation of lightweight functional core materials under multiaxial loading, this study proposes a threshold-shift boundary evolution (TSBE) method. In this method, material distribution is described by a continuous topological potential field, and the boun...
A new mathematical model for solving the static skew-symmetric boundary value problem for a layer weakened by two through-holes under sliding clamping of its end faces is presented and a high-precision numerical study demonstrates that the proposed mathematical model is both accurate and efficient.
B. Panchenko, Mykola Severyn· International Scientific Tec...· 0 citations
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