Geometrically nonlinear behavior of initially curved plane slender bars and frames

1977 ◽  
Vol 46 (4) ◽  
pp. 235-244 ◽  
Author(s):  
A. Pisanty
Keyword(s):  
Nonlinear Behavior ◽  
Geometrically Nonlinear

Sources and Propagation of Nonlinearity in a Vibration Isolator With Geometrically Nonlinear Damping

2015 ◽  
Vol 138 (2) ◽  
Author(s):  
J. C. Carranza ◽  
M. J. Brennan ◽  
B. Tang
Keyword(s):  
Vibration Isolation ◽  
Nonlinear Behavior ◽  
High Amplitude ◽  
Nonlinear Damping ◽  
Single Frequency ◽  
Geometrically Nonlinear ◽  
Harmonic Force ◽  
Isolation System ◽  
Linear Spring ◽  
Harmonic Components

In this paper, the behavior of a single degree-of-freedom (SDOF) passive vibration isolation system with geometrically nonlinear damping is investigated, and its displacement and force transmissibilities are compared with that of a linear system. The nonlinear system is composed of a linear spring and a linear viscous damper which are connected to a mass so that the damper is perpendicular to the spring. The system is excited by a harmonic force applied to the mass or a displacement of the base in the direction of the spring. The transmissibilities of the nonlinear isolation system are calculated using analytical expressions for small amplitudes of excitation and by using numerical simulations for high amplitude of excitation. When excited with a harmonic force, the forces transmitted through the spring and the damper are analyzed separately by decomposing the forces in terms of their harmonics. This enables the effects of these elements to be studied and to determine how they contribute individually to the nonlinear behavior of the system as a whole. For single frequency excitation, it is shown that the nonlinear damper causes distortion of the velocity of the suspended mass by generating higher harmonic components, and this combines with the time-varying nature of the damping in the system to severely distort the force transmitted though the damper. The distortion of the force transmitted through the spring is much smaller than that through the damper.

Geometrically Nonlinear Behavior of Space Beam Structures∗

1985 ◽  
Vol 13 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Claudio Borri ◽  
Heinz-Werner Hufendiek
Keyword(s):  
Nonlinear Behavior ◽  
Geometrically Nonlinear ◽  
Beam Structures

An Optimized Approach for Tracing Pre- and Post-Buckling Equilibrium Paths of Space Trusses

2019 ◽  
Vol 19 (04) ◽  
pp. 1950040
Author(s):  
Alireza Habibi ◽  
Shaahin Bidmeshki
Keyword(s):  
Nonlinear Behavior ◽  
Truss Structures ◽  
Equilibrium Path ◽  
Geometrically Nonlinear ◽  
Arc Length ◽  
Space Truss ◽  
Highly Nonlinear ◽  
Post Buckling ◽  
Space Trusses ◽  
Total Lagrangian Formulation

In this paper, a novel optimization-based method is proposed to analyze steel space truss structures undergoing large deformations. The geometric nonlinearity is considered using the total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to the displacement-type constraints. The proposed approach can fully follow the equilibrium path of the geometrically nonlinear space truss structures not only before the limit point, but also after it, namely, including both the pre- and post-buckling paths. Moreover, a direct estimation of the buckling loads and their corresponding displacements is possible by using the method. Particularly, it has been shown that the equilibrium path of a structure with highly nonlinear behavior, multiple limit points, snap-through, and snap-back phenomena can be traced via the proposed algorithm. To demonstrate the accuracy, validity, and robustness of the proposed procedure, four benchmark truss examples are analyzed and the results compared with those by the modified arc-length method and those reported in the literature.

scholarly journals Analytical solutions for geometrically nonlinear trusses

2009 ◽  
Vol 62 (2) ◽  
pp. 205-214 ◽  
Author(s):  
Marcelo Greco ◽  
Carlos Eduardo Rodrigues Vicente
Keyword(s):  
Analytical Solutions ◽  
Analytical Method ◽  
Nonlinear Behavior ◽  
Constitutive Laws ◽  
Geometrically Nonlinear ◽  
Elastic Materials ◽  
Axial Forces ◽  
Hyper Elastic ◽  
Von Mises

This paper presents an analytical method for analyzing trusses with severe geometrically nonlinear behavior. The main objective is to find analytical solutions for trusses with different axial forces in the bars. The methodology is based on truss kinematics, elastic constitutive laws and equilibrium of nodal forces. The proposed formulation can be applied to hyper elastic materials, such as rubber and elastic foams. A Von Mises truss with two bars made by different materials is analyzed to show the accuracy of this methodology.

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