An Explicit Geometric Stiffness Matrix of a Triangular Flat Plate Element for the Geometric Nonlinear Analysis of Shell Structures

2009 ◽  
Author(s):  
J.-T. Chang ◽  
I.-D. Huang
Keyword(s):  
Flat Plate ◽  
Nonlinear Analysis ◽  
Stiffness Matrix ◽  
Shell Structures ◽  
Plate Element ◽  
Geometric Stiffness ◽  
Geometric Nonlinear ◽  
Geometric Nonlinear Analysis

Recent developments in geometrically nonlinear and postbuckling analysis of framed structures

2003 ◽  
Vol 56 (4) ◽  
pp. 431-449 ◽  
Author(s):  
Yeong-Bin Yang ◽  
Jong-Dar Yau ◽  
Liang-Jenq Leu
Keyword(s):  
Rigid Body ◽  
Nonlinear Analysis ◽  
Stiffness Matrix ◽  
Truss Structures ◽  
Simple Extension ◽  
Framed Structures ◽  
Geometric Stiffness ◽  
Geometric Nonlinear ◽  
Iterative Analysis ◽  
Geometric Nonlinear Analysis

Geometric nonlinear analysis of structures is not a simple extension from its counterpart of linear analysis. In this article, some research works conducted primarily in the past two decades on the geometric nonlinear analysis of framed structures that are readily available to the authors, including, in particular, those conducted by the senior author and coworkers, will be briefly reviewed. To highlight the key features of geometric nonlinear analysis, each of the papers cited will be reviewed according to one or more of the following categories: a) analytical or semi-analytical works, b) formulation of incremental nonlinear theory, c) discrete vs connected element and procedure of assembly, d) joint equilibrium conditions in the deformed configuration, e) rigid body test for nonlinear finite elements, f) key phases in incremental-iterative analysis, g) force recovery procedure, h) strategy for incremental-iterative approaches, i) rigid body-qualified geometric stiffness matrix, j) formulation and simulation for curved beam problems, k) special considerations for truss structures, and l) other related considerations. Throughout this article, emphasis will be placed on the theories and procedures leading to solution of the load-deflection response of structures, which may involve multi-looping curves in the postbuckling range. In fact, a nonlinear analysis using incremental-iterative schemes need not be as complicated as we think. If due account can be taken of the rigid body behaviors at each stage, then the whole process of incremental-iterative analysis can be made simpler and more efficient. Even when the postbuckling behavior of structures is of concern, the use of an accurate elastic stiffness matrix plus a rigid-body-qualified geometric stiffness matrix can always yield satisfactory results. There are 122 references cited in this review article.

GEOMETRIC NONLINEAR ANALYSIS OF CABLE STRUCTURES WITH A TWO-NODE CABLE ELEMENT BY GENERALIZED DISPLACEMENT CONTROL METHOD

2007 ◽  
Vol 07 (04) ◽  
pp. 571-588 ◽  
Author(s):  
Y. B. YANG ◽  
JIUNN-YIN TSAY
Keyword(s):  
Nonlinear Analysis ◽  
Stiffness Matrix ◽  
Control Method ◽  
Three Dimensional ◽  
Suspension Bridges ◽  
Single Element ◽  
Long Span ◽  
Geometric Nonlinear ◽  
Generalized Displacement Control Method ◽  
Geometric Nonlinear Analysis

This paper presents a two-node catenary cable element for the analysis of three-dimensional cable-supported structures. The stiffness matrix of the catenary cable element was derived as the inverse of the flexibility matrix, with allowances for selfweight and pretension effects. The element was then included, along with the beam and truss elements, in a geometric nonlinear analysis program, for which the procedure for computing the stiffness matrix and for performing iterations was clearly outlined. With the present element, each cable with no internal joints can be modeled by a single element, even for cables with large sags, as encountered in cable nets, suspension bridges and long-span cable-stayed bridges. The solutions obtained for all the examples are in good agreement with the existing ones, which indicates the accuracy and applicability of the element presented.

Corotational Formulation for Geometric Nonlinear Analysis of Shell Structures by ANDES Elements

2016 ◽  
Vol 16 (03) ◽  
pp. 1450103
Author(s):  
Yi Zhou ◽  
Yuan-Qi Li ◽  
Zu-Yan Shen ◽  
Ying-Ying Zhang
Keyword(s):  
Nonlinear Analysis ◽  
Large Body ◽  
Nonlinear Problems ◽  
Shell Structures ◽  
Global Coordinate System ◽  
Tangent Stiffness Matrix ◽  
Structural Problems ◽  
Geometric Nonlinear ◽  
Nonlinear Structural ◽  
Geometric Nonlinear Analysis

The corotational (CR) kinematic description was a recent method for formulation of geometric nonlinear structural problems. Based on the consistent symmetrizable equilibrated (CSE) CR formulation, a linear triangular flat shell element with three translational and three rotational degrees of freedom (DOFs) at each of the three nodes was derived by the assumed natural deviatoric strain (ANDES) formulation, which can be used to the geometric nonlinear analysis of shell structures with large rotations and small strains. By taking variations of the internal energy with respect to nodal freedoms, the equations for the CR nonlinear finite element, including the tangent stiffness matrix and the internal force vector in the global coordinate system, were derived. The nonlinear equations were solved by using the generalized displacement control (GDC) method. It was shown through numerical examples that combing CR formulation and ANDES elements can accurately solve complex geometric nonlinear problems with large body motions. As revealed by the efficiency and reliability of the ANDES elements in tracing the nonlinear structural load–deflection response, it is demonstrated that some membrane elements and plate elements give better performance in the geometric nonlinear analysis of shell structures.

A model for thin shells in the combined finite-discrete element method

2018 ◽  
Vol 35 (1) ◽  
pp. 377-394 ◽  
Author(s):  
Ivana Uzelac ◽  
Hrvoje Smoljanovic ◽  
Milko Batinic ◽  
Bernardin Peroš ◽  
Ante Munjiza
Keyword(s):  
Numerical Model ◽  
Discrete Element Method ◽  
Nonlinear Analysis ◽  
Thin Shell ◽  
Discrete Element ◽  
Shell Structures ◽  
Content Type ◽  
Geometric Nonlinear ◽  
Large Rotations ◽  
Geometric Nonlinear Analysis

Purpose This paper aims to present a new numerical model for geometric nonlinear analysis of thin-shell structures based on a combined finite-discrete element method (FDEM). Design/methodology/approach The model uses rotation-free, three-node triangular finite elements with exact formulation for large rotations, large displacements in conjunction with small strains. Findings The presented numerical results related to behaviour of arbitrary shaped thin shell structures under large rotations and large displacement are in a good agreement with reference solutions. Originality/value This paper presents new computationally efficient numerical model for geometric nonlinear analysis and prediction of the behaviour of thin-shell structures based on combined FDEM. The model is implemented into the open source FDEM package “Yfdem”, and is tested on simple benchmark problems.

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