Some obstacle problems for partially hinged plates and related optimization issues

2025/11/06 by Elvise Berchio, Berchio, Elvise, Filomena Feo +3
Computer Science · Engineering · #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Optimization and Control (math.OC) #Structural Response to Dynamic Loads #Topology Optimization in Engineering

paper · pdf · doi:10.48550/arxiv.2511.04287

openalex publication_date 2025/11/06 · openalex created_date 2025/11/08 · openalex updated_date 2026/07/28

Abstract

We study optimization problems for partially hinged rectangular plates, modeling bridge roadways, in the presence of real and artificial obstacles. Real obstacles represent structural constraints to avoid, while artificial ones are introduced to enhance stability. For the former, aiming to prevent collisions, we set up a worst-case optimization problem in which we minimize the amplitude of oscillations with respect to the density distribution; for the latter, aiming to improve the torsional stability, we minimize, with respect to the obstacles, the maximum of a gap function quantifying the displacement between the long edges of the plate. For both problems, existence results are provided, along with a discussion about qualitative properties of optimal density distributions and obstacles.

Citations

• A biharmonic analogue of the Alt-Caffarelli problem
• A positivity preserving property result for the biharmonic operator under partially hinged boundary conditions
• Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates
• A free boundary problem driven by the biharmonic operator
• On the variation of longitudinal and torsional frequencies in a\n partially hinged rectangular plate
• The two obstacle problem for the parabolic biharmonic equation
• Structural instability of nonlinear plates modelling suspension bridges: mathematical answers to some long-standing questions
• Weak uniqueness and partial regularity for the composite membrane problem

Related

• A measure of the torsional performances of partially hinged rectangular\n plates
• Non-homogeneous density functions to strengthen rectangular partially hinged plates
• Instability of modes in a partially hinged rectangular plate
• Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates
• Solving Obstacle Problems using Optimal Homotopy Asymptotic Method