[Paper Review] Algorithms for 2D Mesh Decomposition in Distributed Design Optimization

Shuvodeep De, Rakesh K. Kapania|arXiv (Cornell University)|Feb 3, 2020

Advanced Aircraft Design and Technologies25 references4 citations

TL;DR

This paper presents a coordinate-free, set-based algorithm for decomposing 2D finite element meshes into localized panels for distributed multidisciplinary design optimization (MDO), using elemental connectivity operations to extract panels bounded by arbitrary shapes. The method enables efficient panel extraction and stiffener integration in aircraft wing structures, demonstrating effectiveness in a distributed MDO framework with curvilinear spars and ribs (SpaRibs).

ABSTRACT

Optimization of thin-walled structures like an aircraft wing, aircraft fuselage or submarine hull often involves dividing the shell surface into numerous localized panels, each characterized by its own set of design variables. The process of extracting information about a localized panel (nodal coordinates, mesh connectivity) from a finite element model, input file is usually a problem-specific task. In this work, a generalized process to extract localized panels from the two-dimensional (2D) mesh is discussed. The process employs set operations on elemental connectivity information and is independent of nodal coordinates. Thus, it is capable of extracting panel of any shape given the boundary and thus can be used during optimization of a wide range of structures. A method to create stiffeners on the resulting local panels is also presented, and the effect of stiffener element size on buckling is studied. The local panel extraction process is demonstrated by integrating it into a distributed MDO framework for optimization of an aircraft wing having curvilinear spars and ribs (SpaRibs). A range of examples is included wherein the process is used to create panels on the wing-skin, bounded by adjacent SpaRibs.

Motivation & Objective

• Address the challenge of automating localized panel extraction from 2D meshes in structural optimization, particularly for thin-walled aerospace components.
• Develop a generalized, geometry-agnostic method to extract panels of arbitrary shape from finite element models without relying on nodal coordinates.
• Enable integration into distributed MDO frameworks by decoupling panel generation from geometric modeling.
• Support the creation and analysis of stiffened panels to study buckling behavior under varying stiffener element sizes.
• Demonstrate the method’s applicability in a realistic aircraft wing optimization scenario with curvilinear spars and ribs (SpaRibs).

Proposed method

• Formulate panel extraction as a set operation on elemental connectivity, using only element-to-element adjacency information, independent of nodal coordinates.
• Define boundary curves as sequences of edges to specify panel regions, enabling extraction of panels bounded by complex or irregular shapes.
• Construct local panels by identifying all elements enclosed within a closed boundary using connectivity-based region growing or inclusion checks.
• Integrate a stiffener generation algorithm that places beam elements on the panel edges, with size controlled by user-defined parameters.
• Apply the decomposition pipeline within a distributed MDO framework, allowing independent optimization of each panel with shared global constraints.
• Validate the method on a wing-skin model with SpaRibs, using a range of boundary configurations and stiffener sizes.

Experimental results

Research questions

• RQ1 Can a coordinate-free, connectivity-based algorithm reliably extract localized 2D mesh panels of arbitrary shape from a global finite element model?
• RQ2 How does the size of stiffener elements affect the buckling performance of the extracted panels in a structural optimization context?
• RQ3 To what extent can the proposed mesh decomposition method be integrated into a distributed MDO framework for complex aerospace structures?
• RQ4 What is the computational efficiency and robustness of the algorithm across diverse panel geometries and mesh types?
• RQ5 How does the method preserve structural fidelity and design variable independence when decomposing complex shell-like surfaces?

Key findings

• The proposed mesh decomposition method successfully extracts localized panels of arbitrary shape using only elemental connectivity, without requiring nodal coordinate information.
• The algorithm demonstrates robustness across a range of panel geometries, including non-convex and irregular boundaries, in the context of an aircraft wing model.
• Stiffener element size significantly influences buckling performance, with finer discretization leading to higher critical buckling loads due to better stress distribution.
• The method enables seamless integration into a distributed MDO framework, allowing independent optimization of each panel while maintaining global consistency.
• The approach reduces dependency on CAD geometry during optimization, enabling faster and more flexible design exploration in complex structures.
• The implementation was successfully applied to a wing-skin model bounded by SpaRibs, validating its practical utility in real-world aerospace design scenarios.