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Unsymmetric Loading of Thin-Walled Members: Problem Solving

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The shear center of a channel section with uniform thickness, height, and width, is determined by computing the shear force in the member and calculating the moments of inertia of the sections.
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In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution of...

Unsymmetric Loading of Thin-Walled Members

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Thin-walled members with non-symmetrical cross-sections are vital to engineering structures, offering material efficiency and structural integrity. However, unsymmetrical loading on these members leads to complex stress distributions, resulting in simultaneous bending and twisting can cause deformation or structural failure. The interaction between bending and twisting requires detailed analysis to ensure structural resilience.
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Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

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A Dynamic Programming Setting for Functionally Graded Thick-Walled Cylinders.

Hassan Mohamed Abdelalim Abdalla¹, Daniele Casagrande¹, Francesco De Bona¹

¹Polytechnic Department of Engineering and Architecture, University of Udine, Via Delle Scienze, 206, 33100 Udine, Italy.

Materials (Basel, Switzerland)

|September 12, 2020

Summary

This study optimizes material properties in pressurized cylinders using dynamic programming. Optimal Young

Keywords:

FG cylinder Pontryagin’s principle dynamic programming optimal Young’s modulus

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Area of Science:

Solid Mechanics
Materials Science
Optimization Theory

Background:

Thick-walled cylinders under internal pressure experience non-uniform stress distributions.
Material property variation is crucial for optimizing structural performance.
Functionally graded materials offer tailored mechanical responses.

Purpose of the Study:

To investigate material property variation in internally pressurized thick-walled cylinders.
To determine optimal material distribution for stress reduction.
To apply dynamic programming and optimal control theory to material design.

Main Methods:

Formulation of a state space model based on the plane stress hypothesis.
Application of Pontryagin's Principle to solve the optimal control problem.
Analysis of linear, elastic, isotropic, and radially graded materials.

Main Results:

The optimal Young's modulus distribution is piecewise linear along the radial direction.
Investigation into the potential existence of switching points in the optimal solution.
Numerical examples demonstrate significant equivalent stress reduction.

Conclusions:

Dynamic programming provides an effective framework for optimizing material properties in thick-walled cylinders.
Piecewise linear material grading can lead to improved stress management.
The proposed method shows promise for enhancing the performance of pressure vessels.