Geometric nonlinear analysis of laminated composite stiffened panels using Variational Asymptotic Method. | Shiv Nadar University
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Geometric nonlinear analysis of laminated composite stiffened panels using Variational Asymptotic Method.

The main objective of this work is the development of a new methodology called constraint method for the analysis of laminated composite stiffened structures in an asymptotically accurate manner using Variational Asymptotic Method (VAM). As an application of VAM, the geometric nonlinear analysis of stiffened structures is performed to analyze their nonlinear behavior in terms of load-deformation response curves. The development of VAM begins with the 3D nonlinear problem, which is split into a one dimensional nonlinear analysis (through-the-thickness) and a two dimensional nonlinear plate/shell analysis.

Dimensional reduction process is carried out for reproducing the 3D nonlinear problem to an asymptotically equivalent 2D problem (reference surface). This procedure is implemented by reproducing the 3D strain energy stored in the three dimensional structure from a 2D (reference surface) formulation. VAM is applied to perform this dimensional reduction process based on a rigorous mathematical approach by taking the advantage of small parameters defined in the problem definition (the ratio of thickness to shortest wavelength of the plate/shell reference surface, and strains). Through-the-thickness analysis provides an asymptotically correct 2D constitutive law (closed form analytical expressions) and 3D warping solutions. This 2D nonlinear constitutive law is provided as an input to the plate/shell analysis.

The composite stiffened panel is analyzed by applying VAM to the both skin and stiffener. Through-the-thickness analysis provides an asymptotically correct 2D constitutive law. Then, these 2D constitutive laws of skin and stiffener are provided as an input to the 2D geometric nonlinear analysis. In 2D geometric nonlinear plate/shell analysis, the 2D constitutive law of stiffener and skin are assigned to the associated finite elements to obtain combined global stiffness matrix, then constraint method is applied to form the stiffened structure. This constraint method is developed for the effective integration of the skin and stiffener. The 3D displacement continuity conditions, at the skin and stiffener interface, are the building blocks for developing constraint method. Therefore, the important step of constraint method is to establish a mathematical connectivity between the skin and stiffener to interact both skin and stiffener in a realistic manner.

In the process of implementation of constraint method, a system of so-called constraint relations are developed by applying the 3D displacement continuity conditions at the skin and stiffener interface. Mathematical matrix operations are necessary to develop these 3D displacement continuity conditions. Therefore, a constraint matrix is introduced to incorporate these 3D displacement continuity conditions (constraint relations).The proposed approach is effective and reliable to address the complexity in analyzing stiffened structures. This methodology is developed using a computational symbolic tool, MathematicaR and an implemented computer program named as NASSVAM (Nonlinear Analysis of Stiffened Structures using Variational Asymptotic Method). The obtained results from NASSVAM are compared, and have showed good agreement with the 3D FEA results.

Mechanical Engineering
Student Name: 
Kamineni Jagath Narayana
Faculty Advisor: