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Jan 1, 2012 · The formulation of geometrically exact theories for thin plates, their approximations and differences with respect to either linear or ad hoc nonlinear theories (such as the Föppl–von Karman theory) are presented. The equations of motion are modified for various situations and are compared with experimental results.
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Large Deflection of Homogeneous Isotropic Plates. Application of the von Kármán theory for large-deflection motion of homogeneous, isotropic, rectangular plates is now considered. The problem can be formulated in terms of the middle surface displacement components \ ( { {u}^0}, { {v}^0},w \) or in terms of the Airy stress function \ ( F ...
- tauchert@uky.edu
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- Strain-displacement relations for nonlinear plate theory
- IVW N u
- N n u N w n w M n
- wdS T u Q w M
- n w ,
- M n w n w t ds
- M w ds
- L 0 L
- Nonlinear plate behavior—coupled bending and stretching
The chief characteristic of a thin flat plate is it flexibility for out of plane bending relative to its stiffness with respect to in-plane deformations. The theory we will derive is restricted to small strains, moderate out-of-plane rotations and small in-plane rotations. Analogous to the theory derived for curved beams, a 2D theory will be deri...
, N w , w M , , w dS S
w M n , , , w ds C Notation is displayed in the figure. Next define the external virtual work, EVW : EVW
n , ds P w S C The dead load contributions are as follows (see the figure): the normal pressure distribution, p , the in- plane edge resultant tractions (force/length) , T , the normal edge force/length, Q, and the component of the edge moment that works through the negative of w ,
n . The possibility of concentrated loads acting perpendicular to the plate away from the edge is also noted but it will not be explicitly taken into account below. The reason for the notation will become clearer below. One might be tempted to include a contribution like , w t M ( w , t w , t )—see figure, but we will see that this d...
, n , t C C Let M M n and integrate the second term by parts using ( ) , ( ) t , t
t M wds M w t , t , t t A C C where the contributions at A are meant to represent points along C such as corners at which t is discontinuous. Thus, the troublesome term in IVW becomes M w ds C w ds M n n w M , , n t , t C w corners And we may finally write the internal virtual work as IVW N u ...
The series can be differentiated term by term to give df ( x n
As an introduction to the coupling between bending and stretching in plates we first consider the coupling for an initially straight, simply supported beam within the context of small strain/moderate rotation theory. Two in-plane support conditions will be considered—unconstrained and constrained, as illustrated in the accompanying figure. The gov...
- 621KB
- 33
Jan 1, 2020 · Definition. In the case of the Föppl-von Kármán plate theory, the deflections of the plate are assumed to be moderate (deflections have the same order like the plate thickness), and the plane stress state equations are no more decoupled from the plate equations. The kinematical relations partly take into account nonlinear terms, and the ...
- Holm Altenbach
- holm.altenbach@ovgu.de
May 18, 2022 · The Föppl–von Kármán (FvK) equations are a set of nonlinear partial differential equations describing the large deflection of linear elastic plates [1,2]. They can be derived as a formal asymptotic expansion of the three-dimensional filed theory of linear elasticity in the limit of large displacements and small strains, and associated with ...
The Föppl–von Kármán equations, named after August Föppl [1] and Theodore von Kármán, [2] are a set of nonlinear partial differential equations describing the large deflections of thin flat plates. [3] With applications ranging from the design of submarine hulls to the mechanical properties of cell wall, [4] the equations are ...
Mar 4, 2024 · 4.0/). Abstract: The discovery of the law of the wall, the log-law including the von Kármán constant, is seen to be one of the biggest accomplishments of fluid mechanics. However, after more than ninety years, there is still a controversial debate about the validity and universality of the law of the wall.
