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Abstract
The importance of knowing critical loads and post-critical behavior of thin-walled structures motivates the development of several scientific and practical studies. Most references are concerned with stability analysis for small displacements (first order approach), or with second order stability analyzes, a less precise geometric nonlinear strategy. However, very flexible structures or ones that present small loss of stiffness after the first critical load need more careful analysis. Here we present a shell numerical formulation capable of carrying out stability analysis of thin-walled structures developing large displacements. This formulation uses generalized unconstrained vectors as nodal parameters instead of rotations. To make possible a complete stability analysis using unconstrained vectors, we present an original strategy that imposes a Conjugate Modal Force at the vicinity of critical points, allowing an accurate choice of post-critical paths. Non-conservative forces are also considered and results are compared with literature benchmarks, demonstrating the accuracy and capacity of the proposed formulation.
Highlights
Classical studies (Bleich, 1952; Timoshenko and Gere, 1961; Murray, 1986; Bazant and Cedolin, 1991) analyzing structures with simple geometry and boundary conditions have shown the considerable effect of the presence of imperfections in the achieved critical loads
In order to make possible the stability analysis using unconstrained vectors, in this study we present an original strategy that imposes a Conjugate Modal Force at the vicinity of structural critical points, allowing an accurate choice of post-critical paths by the arc-length method including non-conservative loads (Crisfield, 1981; Feng et al, 1996)
A total Lagrangian nonlinear geometric shell formulation with kinematics described by generalized vectors and positions was proposed and applied in the analysis of equilibrium paths passing through bifurcation points and considering non-conservative loads
Summary
The stability of thin-walled structures is studied by several important works of today and the last decades. The use of numerical methods to analyze structural stability is indispensable when more general geometry and boundary conditions are considered In this sense one may cite, among others, works related to the Finite Strip Methods (FSM) and Generalized Beam Theory (GBT). Applications related to the stability of thin-walled structures are present, for example, in Anbarasu and Sukumar (2014), Ghumare and Sayyad (2017) and Soares et al (2019) These works verify the presence of limit points and bifurcations along the equilibrium path. In order to make possible the stability analysis using unconstrained vectors, in this study we present an original strategy that imposes a Conjugate Modal Force at the vicinity of structural critical points, allowing an accurate choice of post-critical paths by the arc-length method including non-conservative loads (Crisfield, 1981; Feng et al, 1996). Numerical examples explore equilibrium paths that have bifurcations, including pressurized tubes, proving the accuracy and applicability of the proposed technique
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