Nonlinear static isogeometric analysis of arbitrarily curved Kirchhoff-Love shells

08/12/2020
by   G. Radenković, et al.
0

The geometrically rigorous nonlinear analysis of elastic shells is considered in the context of finite, but small, strain theory. The research is focused on the introduction of the full shell metric and examination of its influence on the nonlinear structural response. The exact relation between the reference and equidistant strains is employed and the complete analytic elastic constitutive relation between energetically conjugated forces and strains is derived via the reciprocal shift tensor. Utilizing these strict relations, the geometric stiffness matrix is derived explicitly by the variation of the unknown metric. Moreover, a compact form of this matrix is presented. Despite the linear displacement distribution due to the Kirchhoff-Love hypothesis, a nonlinear strain distribution arises along the shell thickness. This fact is sometimes disregarded for the nonlinear analysis of thin shells based on the initial geometry, thereby ignoring the strong curviness of a shell at some subsequent configuration. We show that the curviness of a shell at each configuration determines the appropriate shell formulation. For shells that become strongly curved at some configurations during deformation, the nonlinear distribution of strain throughout the thickness must be considered in order to obtain accurate results. We investigate four computational models: one based on the full analytical constitutive relation, and three simplified ones. Robustness, efficiency and accuracy of the presented formulation are examined via selected numerical experiments. Our main finding is that the employment of the full metric is often required when the complete response of the shells is sought, even for the initially thin shells. Finally, the simplified model that provided the best balance between efficiency and accuracy is suggested for the nonlinear analysis of strongly curved shells.

READ FULL TEXT

page 22

page 23

page 24

page 27

page 28

research
03/29/2021

Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli-Euler beam

We present a geometrically exact nonlinear analysis of elastic in-plane ...
research
09/21/2021

Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli-Euler beam

The objective of this research is the development of a geometrically exa...
research
06/21/2022

Isogeometric Analysis of Elastic Sheets Exhibiting Combined Bending and Stretching using Dynamic Relaxation

Shells are ubiquitous thin structures that can undergo large nonlinear e...
research
02/02/2021

An enhanced parametric nonlinear reduced order model for imperfect structures using Neumann expansion

We present an enhanced version of the parametric nonlinear reduced order...
research
11/16/2020

A Novel Numerical Method for Modeling Anisotropy in Discretized Bond-Based Peridynamics

This work proposes a novel, general and robust method of determining bon...

Please sign up or login with your details

Forgot password? Click here to reset