Instability of Discrete Pseudo-Conservative Structural Systems

1991 ◽  
Vol 44 (11S) ◽  
pp. S194-S198 ◽  
Author(s):  
Anibal E. Mirasso ◽  
Luis A. Godoy
Keyword(s):  
Classical System ◽  
Potential Energy Function ◽  
Structural Systems ◽  
Equilibrium Path ◽  
Equilibrium Equations ◽  
Total Potential ◽  
Approximate Form ◽  
Nonlinear Equilibrium ◽  
Mechanical Models ◽  
New Formulation

Critical and postcritical states of pseudo-conservative discrete structural systems are studied by means of a new formulation leading to a classification of critical states and to an approximate form of the postcritical equilibrium path. The nonlinear equilibrium equations are derived from the total potential energy function of a classical system, but with the addition of at least one control parameter. The follower force effect is thus included by nonlinear constraints to the equilibrium equation. The nonlinear equations are solved by perturbation techniques. Finally the theory is applied to investigate the instability of some simple mechanical models.

The Effect of Porosity on Elastic Stability of Toroidal Shell Segments Made of Saturated Porous Functionally Graded Materials

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Hadi Babaei ◽  
Mohsen Jabbari ◽  
M. Reza Eslami
Keyword(s):  
Elastic Stability ◽  
Functionally Graded ◽  
Toroidal Shell ◽  
Geometrical Parameters ◽  
Equilibrium Equations ◽  
Closed Form Solutions ◽  
Porous Shell ◽  
Total Potential ◽  
Nonlinear Equilibrium ◽  
The Stability

Abstract This research deals with the stability analysis of shallow segments of the toroidal shell made of saturated porous functionally graded (FG) material. The nonhomogeneous material properties of porous shell are assumed to be functionally graded as a function of the thickness and porosity parameters. The porous toroidal shell segments with positive and negative Gaussian curvatures and nonuniform distributed porosity are considered. The nonlinear equilibrium equations of the porous shell are derived via the total potential energy of the system. The governing equations are obtained on the basis of classical thin shell theory and the assumptions of Biot's poroelasticity theory. The equations are a set of the coupled partial differential equations. The analytical method including the Airy stress function is used to solve the stability equations of porous shell under mechanical loads in three cases. Porous toroidal shell segments subjected to lateral pressure, axial compression, and hydrostatic pressure loads are analytically analyzed. Closed-form solutions are expressed for the elastic buckling behavior of the convex and concave porous toroidal shell segments. The effects of porosity distribution and geometrical parameters of the shell on the critical buckling loads of porous toroidal shell segments are studied.

An Accurate and Efficient Augmented Finite Element Method for Arbitrary Crack Interactions

2013 ◽  
Vol 80 (4) ◽  
Author(s):  
W. Liu ◽  
Q. D. Yang ◽  
S. Mohammadizadeh ◽  
X. Y. Su ◽  
D. S. Ling
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Degrees Of Freedom ◽  
Piecewise Linear ◽  
Single Element ◽  
Dramatic Improvement ◽  
Equilibrium Equations ◽  
Nonlinear Equilibrium ◽  
New Formulation ◽  
Element Method

This paper presents a new augmented finite element method (A-FEM) that can account for path-arbitrary, multiple intraelemental discontinuities with a demonstrated improvement in numerical efficiency by two orders of magnitude when compared to the extended finite element method (X-FEM). We show that the new formulation enables the derivation of explicit, fully condensed elemental equilibrium equations that are mathematically exact within the finite element context. More importantly, it allows for repeated elemental augmentation to include multiple interactive cracks within a single element without additional external nodes or degrees of freedom (DoFs). A novel algorithm that can rapidly and accurately solve the nonlinear equilibrium equations at the elemental level has also been developed for cohesive cracks with piecewise linear traction-separation laws. This efficient new solving algorithm, coupled with the mathematically exact elemental equilibrium equation, leads to dramatic improvement in numerical accuracy, efficiency, and stability when dealing with arbitrary cracking problems. The A-FEM's excellent capability in high-fidelity simulation of interactive cohesive cracks in homogeneous and heterogeneous solids has been demonstrated through several numerical examples.

Mechanical behaviour of bistable struts

2011 ◽  
Vol 226 (5) ◽  
pp. 1321-1325 ◽  
Author(s):  
J G Cai ◽  
Y X Xu ◽  
J Feng ◽  
J Zhang
Keyword(s):  
Mechanical Behaviour ◽  
Displacement Curve ◽  
Equilibrium Path ◽  
Equilibrium Equations ◽  
Structural Element ◽  
Total Potential ◽  
Bifurcation Buckling ◽  
The Stability ◽  
Von Mises ◽  
Joint Behaviour

The mechanical behaviour of a bistable structural element, which is based on the snap-through and bifurcation properties of the von Mises truss, has been investigated in this article. By assuming the joint behaviour as ideal hinges and using the large deformation theory based on a linear elastic material, a simple analytical model for the stability of the von Mises truss was formulated. The governing set of non-linear equilibrium equations was obtained by applying the principle of stationary total potential energy. Then, the formulae of the snap-through and bifurcation buckling loads and the equilibrium path were given. In addition to the well-known cases of primary and secondary branches, a third type that the bifurcation buckling point lying on the descending branch of the load versus displacement curve was discussed. In this case, although its upper bifurcation load is lower than its upper snap-through buckling load, the truss experiences a symmetric snap-through mode first, and hence the bifurcation point is not physically relevant. Finally, the assumptions of the classical von Mises truss analysis are discussed.

A solution method of equilibrium equations for large structural systems

1985 ◽  
Vol 20 (1-3) ◽  
pp. 107-114 ◽  
Author(s):  
T.C. Cheu ◽  
C.P. Johnson ◽  
R.R. Craig
Keyword(s):  
Solution Method ◽  
Structural Systems ◽  
Equilibrium Equations

NONLINEAR GENERALIZED BEAM THEORY FOR COLD-FORMED STEEL MEMBERS

2003 ◽  
Vol 03 (04) ◽  
pp. 461-490 ◽  
Author(s):  
N. SILVESTRE ◽  
D. CAMOTIM
Keyword(s):  
Numerical Technique ◽  
Beam Theory ◽  
Equilibrium Equations ◽  
Steel Members ◽  
Mode Decomposition ◽  
Nonlinear Equilibrium ◽  
Geometrical Imperfections ◽  
Post Buckling ◽  
Cold Formed Steel ◽  
Generalized Beam Theory

A geometrically nonlinear Generalized Beam Theory (GBT) is formulated and its application leads to a system of equilibrium equations which are valid in the large deformation range but still retain and take advantage of the unique GBT mode decomposition feature. The proposed GBT formulation, for the elastic post-buckling analysis of isotropic thin-walled members, is able to handle various types of loading and arbitrary initial geometrical imperfections and, in particular, it can be used to perform "exact" or "approximate" (i.e., including only a few deformation modes) analyses. Concerning the solution of the system of GBT nonlinear equilibrium equations, the finite element method (FEM) constitutes the most efficient and versatile numerical technique and, thus, a beam FE is specifically developed for this purpose. The FEM implementation of the GBT post-buckling formulation is reported in some detail and then employed to obtain numerical results, which validate and illustrate the application and capabilities of the theory.

scholarly journals Optimal Shape and First Integrals for Inverted Compressed Column

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 334
Author(s):  
Enes Kacapor ◽  
Teodor M. Atanackovic ◽  
Cemal Dolicanin
Keyword(s):  
Variational Principle ◽  
First Integrals ◽  
Arbitrary Cross Section ◽  
Optimal Shape ◽  
Equilibrium Equations ◽  
Concentrated Force ◽  
Cross Sectional ◽  
Nonlinear Equilibrium ◽  
Elastic Column ◽  
Special Case

We study optimal shape of an inverted elastic column with concentrated force at the end and in the gravitational field. We generalize earlier results on this problem in two directions. First we prove a theorem on the bifurcation of nonlinear equilibrium equations for arbitrary cross-section column. Secondly we determine the cross-sectional area for the compressed column in the optimal way. Variational principle is constructed for the equations determining the optimal shape and two new first integrals are constructed that are used to check numerical integration. Next, we apply the Noether’s theorem and determine transformation groups that leave variational principle Gauge invariant. The classical Lagrange problem follows as a special case. Several numerical examples are presented.

NUMERICAL ANALYSIS OF CIRCULAR CONCRETE-FILLED STEEL TUBULAR SLENDER BEAM-COLUMNS WITH PRELOAD EFFECTS

2013 ◽  
Vol 13 (03) ◽  
pp. 1250065 ◽  
Author(s):  
VIPULKUMAR ISHVARBHAI PATEL ◽  
QING QUAN LIANG ◽  
MUHAMMAD N. S. HADI
Keyword(s):  
Numerical Model ◽  
Order Effects ◽  
Computational Algorithms ◽  
Equilibrium Equations ◽  
Steel Tubes ◽  
Beam Columns ◽  
Concrete Confinement ◽  
Nonlinear Equilibrium ◽  
Initial Geometric Imperfections ◽  
Loading Eccentricity

This paper presents a new numerical model for the nonlinear analysis of circular concrete-filled steel tubular (CFST) slender beam-columns with preload effects, in which the initial geometric imperfections, deflections caused by preloads, concrete confinement and second order effects are incorporated. Computational algorithms are developed to solve the nonlinear equilibrium equations. Comparative studies are undertaken to validate the accuracy of computational algorithms developed. Also included is a parametric study for examining the effects of the preloads, column slenderness, diameter-to-thickness ratio, loading eccentricity, steel yield stress and concrete confinement on the behavior of circular CFST slender beam-columns under eccentric loadings. The numerical model is demonstrated to be capable of predicting accurately the behavior of circular CFST slender beam-columns with preloads. The preloads on the steel tubes can affect significantly the behavior of CFST slender beam-columns and must be taken into account in the design.

Effects of rotor blade-tip geometry on helicopter trim and control response

2017 ◽  
Vol 121 (1239) ◽  
pp. 637-659 ◽  
Author(s):  
M. Rohin Kumar ◽  
C. Venkatesan
Keyword(s):  
Equations Of Motion ◽  
Rotor Blades ◽  
Equilibrium Equations ◽  
Aerodynamic Model ◽  
Nonlinear Equilibrium ◽  
Control Response ◽  
Blade Tip ◽  
Nonlinear Equations Of Motion ◽  
The Cost ◽  
And Control

ABSTRACTFor performance improvement and noise reduction, swept and anhedral tips have been incorporated in advanced-geometry rotor blades. While there are aerodynamic benefits to these advanced tip geometries, they come at the cost of complicated structural design and weight penalties. The effect of these tip shapes on loads, vibration and aeroelastic response are also unclear. In this study, a comprehensive helicopter aeroelastic analysis which includes rotor-fuselage coupling shall be described and the analysis results for rotor blades with straight tip, tip sweep and tip anhedral shall be presented and compared. The helicopter modelled is a conventional one with a hingeless single main rotor and single tail rotor. The blade undergoes flap, lag, torsion and axial deformations. Tip sweep, pretwist, precone, predroop, torque offset and root offset are included in the model. Aerodynamic model includes Peters-He dynamic wake theory for inflow and the modified ONERA dynamic stall theory for airloads calculations. The complete 6-dof nonlinear equilibrium equations of the fuselage are solved for analysing any general flight condition. Response to pilot control inputs is determined by integrating the full set of nonlinear equations of motion with respect to time. The effects of tip sweep and tip anhedral on structural dynamics, trim characteristics and vehicle response to pilot inputs are presented. It is shown that for blades with tip sweep and tip anhedral/dihedral, the 1/rev harmonics of the root loads reduce while the 4/rev harmonics of the hub loads increase in magnitude. Tip dihedral is shown to induce a reversal of yaw rate for lateral and longitudinal cyclic input.

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