Meshfree particle methods for analysis of elastic plates and shells

University Of North Carolina At Charlotte, Charlotte NC

Investigators

Abstract

A large number of structural components in engineering can be classified as plates. Typical examples of civil engineering structures are floor and foundation slabs, lock-gates, thin retaining walls, bridge decks, and slab bridges. Plates are also indispensable in ship building, automobile, and aerospace industries. The stress resultants of a thin plate can be calculated through the 3-dimensional elasticity equations. However, under certain hypotheses, the 3-dimensional elasticity equations for a plate are reduced to the 2-dimensional equations. The Kirchhoff plate model is well suited for thin plates. However, the governing equation for the displacement of this plate model is the fourth order differential equation. The conventional finite element method is difficult to apply because of the complexity of constructing smooth finite elements. Furthermore, moderately thick plates have other difficulties such as boundary layer problems and shear locking problems. Meshless methods (in which smooth flexible approximation functions are used and complicated mesh generation is not necessary) have several advantages over the conventional finite element method. However, these methods have several major limitations including the inefficiency in handling essential boundary conditions, large matrix condition numbers, and complexity in constructing partitions of unity. Most recently, the PI invented one of the most flexible closed form partition of unity, called the Generalized Product Partition of Unity. The PI proposes to introduce Meshfree particle methods by using the Generalized Product Partition of Unity, together with new local approximation functions that can handle geometric boundary conditions as well as force boundary conditions arising in various plate models. Furthermore, the PI proposes to apply Meshfree particle methods to obtain highly accurate stress analysis of plates and shells for design and maintenance of related engineering structures. The Intellectual Merit: The proposed research will greatly improve the stress analysis of plates, shells, and laminated composite plates so that design and maintenance of automobiles, airplanes, ships, and all other engineering structures related to plates and shells may be more effective and safer. Moreover, without any difficulty, the proposed method is able to surgically make the approximation space enriched with any type of singular function. The proposed method is flexible and effective in dealing with singularities and it can be used for accurate prediction of crack propagation. The Broader Impacts: Results from the proposed research can be used to design fuel efficient automobiles, safer airplanes, ships and new materials more resistant to failure. The proposed research can also be applied to improve maintenance of aging airliners, bridges, ships, buildings, and numerous other applications where structural integrity should be closely monitored. Ultimately, the proposed research will have direct impacts on the public safety and the environment by increasing efficiency and safety of common modes of transportation and structures used everyday.