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Free Vibration analysis of Curvilinearly Stiffened Composite plates with an arbitrarily shaped cutout using Isogeometric Analysis

Balakrishnan Devarajan

TL;DR

This paper focuses on the isogeometric vibration analysis of curvilinearly stiffened composite panels and the stiffness matrices and the mass matrices are derived using the first-order shear deformation theory (FSDT).

Abstract

This paper focuses on the isogeometric vibration analysis of curvilinearly stiffened composite panels. The stiffness matrices and the mass matrices are derived using the first-order shear deformation theory (FSDT). The present method models the plate and the stiffener separately, which allows the stiffener element nodes to not coincide with the plate shell-element nodes. The stiffness and mass matrices of a stiffener are transformed to those of the plate through the displacement compatibility conditions at the plate/stiffener interface by interpolation using NURBS basis functions. Cutouts are modeled using a single NURBS patch generated by creating a ruled surface between two curves. The proposed formulation is first validated by comparing it with available literature. The effects of width-to-thickness ratio, fiber orientation, ply layups, shape and size of the cutouts and the boundary conditions on the response of stiffened composite plates are then analyzed and the numerical results are used to derive useful conclusions.

Free Vibration analysis of Curvilinearly Stiffened Composite plates with an arbitrarily shaped cutout using Isogeometric Analysis

TL;DR

This paper focuses on the isogeometric vibration analysis of curvilinearly stiffened composite panels and the stiffness matrices and the mass matrices are derived using the first-order shear deformation theory (FSDT).

Abstract

This paper focuses on the isogeometric vibration analysis of curvilinearly stiffened composite panels. The stiffness matrices and the mass matrices are derived using the first-order shear deformation theory (FSDT). The present method models the plate and the stiffener separately, which allows the stiffener element nodes to not coincide with the plate shell-element nodes. The stiffness and mass matrices of a stiffener are transformed to those of the plate through the displacement compatibility conditions at the plate/stiffener interface by interpolation using NURBS basis functions. Cutouts are modeled using a single NURBS patch generated by creating a ruled surface between two curves. The proposed formulation is first validated by comparing it with available literature. The effects of width-to-thickness ratio, fiber orientation, ply layups, shape and size of the cutouts and the boundary conditions on the response of stiffened composite plates are then analyzed and the numerical results are used to derive useful conclusions.

Paper Structure

This paper contains 13 sections, 31 equations, 9 figures, 14 tables.

Table of Contents

  1. Introduction
  2. Mathematical Foundation
  3. Orthotropic layers
  4. Curvilinear stiffener
  5. Modeling complicated cutouts using a single NURBS patch
  6. A Three point parametrization of the curvilinear stiffener
  7. Results and Discussion
  8. Isotropic plate with a circular hole at the center
  9. Isotropic plate with a complicated cutout
  10. Vibration of a Composite plate with a heart shaped cutout
  11. Curvilinearly stiffened composite panels with central circular cutout
  12. Curvilinearly stiffened composite panels with an elliptical central cutout
  13. Conclusions

Figures (9)

  • Figure 1: Geometry and nomenclature of a stiffened composite panel with a central cutout. Redrawn and modified from Zhao2016
  • Figure 2: Composite plate (red) stiffened by a rectangular stiffener (gray)
  • Figure 4: Inner and the outer curve to generate a plate with a complicated cutout
  • Figure 5: Mesh and connectivity plot of a plate with a complicated cutout
  • Figure 6: Parametrization of curvilinear stiffener
  • ...and 4 more figures