scholarly journals Effects of Geometrical Nonlinearity and Shear Deformations on the Seismic Design Analysis of Steel Piers Based on Nonlinear Beam Model.

2002 ◽  
pp. 157-172
Author(s):  
Yoshiaki GOTO ◽  
Toru OKUMURA ◽  
Masaya SUZUKI
Keyword(s):  
Seismic Design ◽  
Geometrical Nonlinearity ◽  
Design Analysis ◽  
Beam Model ◽  
Shear Deformations ◽  
Nonlinear Beam

Nonlinear Axial and Transverse Oscillation and Control of a PZT Laminated Distributed Structronic System

2000 ◽  
Author(s):  
H. S. Tzou ◽  
J. H. Ding ◽  
W. K. Chai
Keyword(s):  
Distributed Control ◽  
Shape Control ◽  
Geometrical Nonlinearity ◽  
Axial Displacement ◽  
Beam Model ◽  
Control Effect ◽  
Laminated Beam ◽  
Practical Applications ◽  
Axial Oscillation ◽  
And Control

Abstract Piezoelectric laminated distributed systems have broad applications in many new smart structures and structronic systems. As the shape control becomes an essential issue in practical applications, the nonlinear large deformation has to be considered, and thus, the geometrical nonlinearity has to be incorporated. Two electromechanical partial differential equations, one in the axial direction and the other in the transverse direction, are derived for the nonlinear PZT laminated beam model. The conventional approach is to neglect the axial oscillation and distributed sensing and control of the distributed laminated beam is evaluated, excluding the effect of axial oscillation. In this paper, influence of the axial displacement to the dynamics and distributed control effect is evaluated. Analysis results reveal that the axial displacement, indeed, has significant influence to the dynamic and distributed control responses of the nonlinear distributed PZT laminated beam structronics systems.

scholarly journals Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
W. Gafsi ◽  
F. Najar ◽  
S. Choura ◽  
S. El-Borgi
Keyword(s):  
Passive Control ◽  
Inverse Eigenvalue Problem ◽  
Beam Dynamics ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Geometrical Parameters ◽  
Flexible Beam ◽  
Beam Model ◽  
Nonlinear Frequency ◽  
Nonlinear Beam

In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

Appropriate Damping on Seismic Design Analysis for Inelastic Response Assessment of Piping

2018 ◽  
Author(s):  
Tomoyoshi Watakabe ◽  
Masaki Morishita
Keyword(s):  
Seismic Design ◽  
Design Method ◽  
Response Spectrum ◽  
Response Assessment ◽  
Design Analysis ◽  
Stress Factors ◽  
Design Rule ◽  
Inelastic Analysis ◽  
Current Design ◽  
Seismic Design Method

The current seismic design rule on piping assumes elastic analysis without the effect of response reduction due to plasticity, although some degree of plasticity is allowed in its allowable limits. Damping for the seismic design analysis is conservatively determined depending on the number of supports and thermal insulation conditions. These conservative assumptions lead to large amount of design margin. Based on such recognition, to provide a more rational seismic design method, a new Code Case for seismic design of piping is now under development in the framework of JSME Nuclear Codes and Standards as an alternative rule to the current design rule. The Code Case provides detailed inelastic analysis with using shell or solid FEA models as a more rational method. Simplified analysis with an additional damping taking the response reduction due to plasticity into account is now under consideration to incorporate the convenience in design. In this study, a series of analysis was made to see the adequacy of the simplified inelastic analysis. Design margins contained in the current design analysis method composed of response spectrum analysis and stress factors was quantitatively assessed in the view point of additional damping.

scholarly journals Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150790 ◽  
Author(s):  
F. dell’Isola ◽  
I. Giorgio ◽  
M. Pawlikowski ◽  
N. L. Rizzi
Keyword(s):  
Large Deformations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Beam Theory ◽  
Beam Model ◽  
Computationally Efficient ◽  
Nonlinear Beam ◽  
Pantographic Structures ◽  
Diffusion Of Technology ◽  
Second Gradient

The aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call ‘pantographic structures’. The interest in these materials was increased by the possibilities opened by the diffusion of technology of three-dimensional printing. They can be regarded, once choosing a suitable length scale, as families of beams (also called fibres) interconnected to each other by pivots and undergoing large displacements and large deformations. There are, however, relatively few ‘ready-to-use’ results in the literature of nonlinear beam theory. In this paper, we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model. The homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems. Furthermore, we consider pantographic structures, find the corresponding homogenized second gradient deformation energies and study some planar problems. Numerical solutions for these two-dimensional problems are obtained via minimization of energy and are compared with some experimental measurements, in which elongation phenomena cannot be neglected.

scholarly journals BEAM ELEMENT UNDER FINITE ROTATIONS

2021 ◽  
Vol 30 ◽  
pp. 87-92
Author(s):  
Emma La Malfa Ribolla ◽  
Milan Jirásek ◽  
Martin Horák
Keyword(s):  
Cross Sections ◽  
Shooting Method ◽  
Small Strain ◽  
Beam Model ◽  
Equilibrium Equations ◽  
Finite Rotations ◽  
Nonlinear Beam ◽  
Linear Elastic ◽  
Beam Elements ◽  
Large Rotations

The present work focuses on the 2-D formulation of a nonlinear beam model for slender structures that can exhibit large rotations of the cross sections while remaining in the small-strain regime. Bernoulli-Euler hypothesis that plane sections remain plane and perpendicular to the deformed beam centerline is combined with a linear elastic stress-strain law.The formulation is based on the integrated form of equilibrium equations and leads to a set of three first-order differential equations for the displacements and rotation, which are numerically integrated using a special version of the shooting method. The element has been implemented into an open-source finite element code to ease computations involving more complex structures. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

Modeling and Experimentation of a Ribbed Caudal Fin for Aquatic Robots

2017 ◽  
Author(s):  
Oscar Rios ◽  
Ardavan Amini ◽  
Hidenori Murakami
Keyword(s):  
Large Deformation ◽  
Beam Theory ◽  
Fe Model ◽  
Beam Model ◽  
Caudal Fin ◽  
Nonlinear Beam ◽  
Beam Elements ◽  
Side Walls ◽  
Thin Beams ◽  
Shear Deformable

Presented in this study is a mathematical model and preliminary experimental results of a ribbed caudal fin to be used in an aquatic robot. The ribbed caudal fin is comprised of two thin beams separated by ribbed sectionals as it tapers towards the fin. By oscillating the ribbed caudal fin, the aquatic robot can achieve forward propulsion and maneuver around its environment. The fully enclosed system allows for the aquatic robot to have very little effect on marine life and fully blend into its respective environment. Because of these advantages, there are many applications including surveillance, sensing, and detection. Because the caudal fin actuator has very thin side walls, Kirchhoff-Love’s large deformation beam theory is applicable for the large deformation of the fish-fin actuator. In the model, it is critical to accurately model the curvature of beams. To this end, C1 beam elements for thin beams are developed by specializing the shear-deformable beam elements, developed by the authors, based upon Reissner’s shear-deformable nonlinear beam model. Furthermore, preliminary experiments on the ribbed fin are presented to supplement the FE model.

Combination of modal responses in linear spectral method: comparison of different formulae for correlation coefficients

2021 ◽  
pp. 32-42
Author(s):  
Alexander G. Tyapin
Keyword(s):  
Spectral Method ◽  
Static Analysis ◽  
Seismic Design ◽  
Method Comparison ◽  
Correlation Coefficients ◽  
Design Analysis ◽  
Common Method ◽  
The Common ◽  
The One ◽  
Mode Response

Linear-spectral method (LSM) is still the common method for the seismic design analysis. "One-component one-mode" responses, obtained by static analysis in the conventional variant of LSM, are combined twice: first for different modes but for each single excitation component separately, then for the different excitation components. In the alternative LSM variant presented in the Russian code SP 14.13330, first one chooses the "most dangerous" direction of the one-component excitation for each mode; then calculates the "one-mode" response for this excitation, and finally these responses are combined. In both cases the combination is performed using the complete quadratic combination (CQC) rule. Different documents suggest different formulae for the correlation coefficients. In the paper different formulae are compared to each other. The goal is to limit the number of calculated coefficients and decrease the amount of calculations.

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