Blended isogeometric Kirchhoff–Love and continuum shells

Abstract

The computational modeling of thin-walled structures based on isogeometric analysis (IGA), non-uniform rational B-splines (NURBS), and Kirchhoff-Love (KL) shell formulations has attracted significant research attention in recent years. While these methods offer numerous benefits over the traditional finite element approach, including exact representation of the geometry, naturally satisfied high-order continuity within each NURBS patch, and computationally efficient rotation-free formulations, they also present a number of challenges in modeling real-world engineering structures of considerable complexity. Specifically, these NURBS-based engineering models are usually comprised of numerous patches, with discontinuous derivatives, nonconforming discretizations, and non-watertight connections at their interfaces. Moreover, the analysis of such structures often requires the full stress and strain tensors (i.e., including the transverse normal and shear components) for subsequent failure analysis and remaining life prediction. Despite the efficiency provided by the KL shell, the formulation cannot accurately predict the response in the transverse directions due to its kinematic assumptions. In this work, a penalty-based formulation for the blended coupling of KL and continuum shells is presented. The proposed approach embraces both the computational efficiency of KL shells and the availability of the full-scale stress/strain tensors of continuum shells where needed by modeling critical structural components using continuum shells and other components using KL shells. The proposed method enforces the displacement and rotational continuities in a variational manner and is applicable to non-conforming and non-smooth interfaces. The efficacy of the developed method is demonstrated through a number of benchmark studies with a variety of analysis configurations, including linear and nonlinear analyses, matching and non-matching discretizations, and isotropic and composite materials. Finally, an aircraft horizontal stabilizer is considered to demonstrate the applicability of the proposed blended shells to real-world engineering structures of significant complexity. c

Nonlinear continuum mechanics of thick hyperelastic sandwich beams using various shear deformable beam theories

“…(Studies on layered structures based on various thickness assumptions can be found in Refs. [44][45][46][47][48][49][50].) For pinned-pinned and fixed-fixed boundary conditions, these trial functions are written as…”

Analysis of the openings of aircraft composite laminated wing beam web under shear load

“…The number of layers, thickness and direction are exactly the same, the boundary conditions are the same, and the applied loads are all the cutting force of 100 N/mm, the opening area is the same, both are 10000 mm². The web models of triangular, rhombic and circular open beams were established for simulation analysis [16].…”

A Geometrically Exact Triangular Shell Element Based on Reproducing Kernel DMS-Splines

“…Over the past few years, many IGA based Kirchhoff-Love rectangular shell elements [2,12,14,37,40,41] have been proposed. However, the application of these elements is limited because a single B-spline/NURBS patch can only represent the surfaces of rectangular topological type.…”