arXiv subjects

Shafeequdheen P

Publications and source records attributed to Shafeequdheen P.

4 recordsLinked to original sources

arXiv2026

Assessing Finite Element Choice in Structural Topology Optimization and A Posteriori Error Estimation

This study investigates the impact of finite element selection on structural topology optimization using the SIMP (Solid Isotropic Material with Penalization) method. Specifically, it compares linear (P1) and quadratic (P2) triangular elements with the conventional bi-linear quadrilateral (Q1) elements. Numerical experiments performed on benchmark problems including a cantilever beam, a bridge structure, and a beveled beam reveal notable differences in both the final optimized objective value (compliance) and the accuracy of the finite element solutions. The accuracy is evaluated using an a posteriori error estimator, highlighting the influence of element type on solution quality and optimization performance.

math.NA↗

arXiv2026

Comparative Analysis of Compliance-Matrix Induced Norms in Structural Topology Optimization

Compliance minimization is a central objective in structural topology optimization, commonly interpreted as the total strain energy of a system. In this work, we examine the influence of alternative compliance formulations based on different norm representations of structural energy. Specifically, we consider three formulations: the classical quadratic compliance, its square-root form corresponding to an l2 norm, and a spectral l1 -norm based formulation derived from the stiffness weighted displacement field. Although these formulations arise from the same stiffness displacement relationship, they generate markedly different optimization landscapes and result in distinct structural topologies. Numerical results indicate that the classical formulation produces well-distributed load paths, whereas the l1 -based formulation promotes sparse and highly localized structural members. These findings underscore the critical role of objective function selection in topology optimization and offer insights into alternative formulations for achieving tailored structural performance.

cs.CE↗

arXiv2025

Diffeomorphic Reconstruction Of A 2D Simple Non Parametric Manifold From Level Set Data Via Shape Gradients

A variational approach to the reconstruction of a shape (2D simple manifolds) as triangulated surface from given level set using shape gradients is presented. It involves an energy functional that depends on the local shape characteristics of the surface. Minimization of the energy through an iterative procedure using the gradient descent method yields a triangulated surface mesh which matches the boundary of the object of interest and this model ensures the smoothness of the boundary.

cs.GR↗

arXiv2025

Shape Gradient Based Non-Parametric Mumford-Shah Segmentation Without Level Sets

A non parametric, level set free method is proposed for detecting image boundaries using the shape gradient of the Mumford Shah energy for segmentation. Minimizing the variance in pixel intensities inside and outside a boundary set of points is the primary pursuit. The boundary set as a polygon of points rather than a parametric form or a level set, evolves under the guidance of a shape gradient of the Mumford Shah piece wise constant segments model. Iteratively updating through the gradient descent method. The proposed method has been tested on various images, demonstrating its effectiveness in capturing intricate and narrow boundaries texture images.

math.AP↗