Validation of Classical Beam and Plate Models by Variational Convergence

2008 ◽  
pp. 177-188 ◽  
Author(s):  
Paolo Podio-Guidugli
Keyword(s):  
Variational Convergence ◽  
Plate Models

Nonlinear thin plate models for a family of Ogden materials

2003 ◽  
Vol 337 (12) ◽  
pp. 819-824 ◽  
Author(s):  
Karim Trabelsi
Keyword(s):  
Thin Plate ◽  
Plate Models

Comparison of nano-plate bending behaviour by Eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models

2018 ◽  
Vol 230 (3) ◽  
pp. 885-907 ◽  
Author(s):  
Y. P. Zhang ◽  
N. Challamel ◽  
C. M. Wang ◽  
H. Zhang
Keyword(s):  
Plate Bending ◽  
Plate Models ◽  
Bending Behaviour

Plate models with state-dependent damping coefficient and their quasi-static limits

2010 ◽  
Vol 73 (6) ◽  
pp. 1626-1644 ◽  
Author(s):  
Igor Chueshov ◽  
Stanislav Kolbasin
Keyword(s):  
Damping Coefficient ◽  
State Dependent ◽  
Plate Models

scholarly journals Approximations of Variational Problems in Terms of Variational Convergence

2017 ◽  
Vol 20 (K2) ◽  
pp. 107-116
Author(s):  
Diem Thi Hong Huynh
Keyword(s):  
Multiobjective Optimization ◽  
Metric Space ◽  
Metric Spaces ◽  
Equilibrium Problems ◽  
Variational Problems ◽  
Dimensional Case ◽  
Variational Convergence ◽  
Finite Dimensional ◽  
Finite Dimensional Case ◽  
Definition Of

We show first the definition of variational convergence of unifunctions and their basic variational properties. In the next section, we extend this variational convergence definition in case the functions which are defined on product two sets (bifunctions or bicomponent functions). We present the definition of variational convergence of bifunctions, icluding epi/hypo convergence, minsuplop convergnece and maxinf-lop convergence, defined on metric spaces. Its variational properties are also considered. In this paper, we concern on the properties of epi/hypo convergence to apply these results on optimization proplems in two last sections. Next we move on to the main results that are approximations of typical and important optimization related problems on metric space in terms of the types of variational convergence are equilibrium problems, and multiobjective optimization. When we applied to the finite dimensional case, some of our results improve known one.

The Static Aeroelasticity of Slender Configurations

1963 ◽  
Vol 14 (1) ◽  
pp. 75-104 ◽  
Author(s):  
G. J. Hancock
Keyword(s):  
Static Stability ◽  
Aerodynamic Forces ◽  
Flexible Aircraft ◽  
The Past ◽  
Plate Models ◽  
Non Linear ◽  
The Future ◽  
Static Aeroelasticity ◽  
Definition Of ◽  
Image Position

SummaryThe validity and applicability of the static margin (stick fixed) Kn,where as defined by Gates and Lyon is shown to be restricted to the conventional flexible aircraft. Alternative suggestions for the definition of static margin are put forward which can be equally applied to the conventional flexible aircraft of the past and the integrated flexible aircraft of the future. Calculations have been carried out on simple slender plate models with both linear and non-linear aerodynamic forces to assess their static stability characteristics.

Nonlocal Approaches for the Vibration of Lattice Plates Including Both Shear and Bending Interactions

2018 ◽  
Vol 18 (07) ◽  
pp. 1850094 ◽  
Author(s):  
F. Hache ◽  
N. Challamel ◽  
I. Elishakoff
Keyword(s):  
Natural Frequencies ◽  
Scale Effects ◽  
Dynamical Behavior ◽  
Mindlin Plate ◽  
Length Scale ◽  
Small Length ◽  
Simply Supported ◽  
Small Length Scale ◽  
Plate Models ◽  
Scale Coefficient

The present study investigates the dynamical behavior of lattice plates, including both bending and shear interactions. The exact natural frequencies of this lattice plate are calculated for simply supported boundary conditions. These exact solutions are compared with some continuous nonlocal plate solutions that account for some scale effects due to the lattice spacing. Two continualized and one phenomenological nonlocal UflyandMindlin plate models that take into account both the rotary inertia and the shear effects are developed for capturing the small length scale effect of microstructured (or lattice) thick plates by associating the small length scale coefficient introduced in the nonlocal approach to some length scale coefficients given in a Taylor or a rational series expansion. The nonlocal phenomenological model constitutes the stress gradient Eringen’s model applied at the plate scale. The continualization process constructs continuous equation from the one of the discrete lattice models. The governing partial differential equations are solved in displacement for each nonlocal plate model. An exact analytical vibration solution is obtained for the natural frequencies of the simply supported rectangular nonlocal plate. As expected, it is found that the continualized models lead to a constant small length scale coefficient, whereas for the phenomenological nonlocal approaches, the coefficient, calibrated with respect to the element size of the microstructured plate, is structure-dependent. Moreover, comparing the natural frequencies of the continuous models with the exact discrete one, it is concluded that the continualized models provide much more accurate results than the nonlocal Uflyand–Mindlin plate models.

Combinations for the Free Vibration Behaviors of Anisotropic Rectangular Plates Under General Edge Conditions

1999 ◽  
Author(s):  
Yoshihiro Narita
Keyword(s):  
Free Vibration ◽  
Structural Design ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Technical Information ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Plate Models ◽  
Edge Conditions ◽  
Anisotropic Rectangular Plates

Abstract The free vibration behavior of rectangular plates provides important technical information in structural design, and the natural frequencies are primarily affected by the boundary conditions as well as aspect and thickness ratios. One of the three classical edge conditions, i.e., free, simple supported and clamped edges, may be used to model the constraint along an edge of the rectangle. Along the entire boundary with four edges, there exist a wide variety of combinations in the edge conditions, each yielding different natural frequencies and mode shapes. For counting the total number of possible combinations, the present paper introduces the Polya counting theory in combinatorial mathematics, and formulas are derived for counting the exact numbers. A modified Ritz method is then developed to calculate natural frequencies of anisotropic rectangular plates under any combination of the three edge conditions and is used to numerically verify the numbers. In numerical experiments, the number of combinations in the free vibration behaviors is determined for some plate models by using the derived formulas, and are corroborated by counting the numbers of different sets of the natural frequencies that are obtained from the Ritz method.

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