Large Displacements With Small Strains in Loaded Structures

1948 ◽  
Vol 15 (1) ◽  
pp. 45-48
Author(s):  
K. H. Swainger
Keyword(s):  
Exact Solution ◽  
Flat Plate ◽  
Large Class ◽  
Major Part ◽  
Flexible Structures ◽  
Elastic Cylinder ◽  
Small Displacement ◽  
Large Displacements ◽  
Physical Conditions ◽  
Small Strains

Abstract This paper considers the case of flexible structures in which displacements can be large although strains are small. The theory gives an “exact” solution in a large class of problems where the displacements are large but predictable closely from the physical conditions imposed. In this method, the major part of the displacement is “guessed,” and then a further “small” displacement calculated from equations, which are developed, to assure compatibility. As a simple but not trivial example, the generation of an elastic cylinder from a flat plate is considered to illustrate the method.

scholarly journals Elément de poutre multicouche avec glissement d’interface

2007 ◽  
pp. 559-581
Author(s):  
Blaise Rebora ◽  
François Frey
Keyword(s):  
Arbitrary Number ◽  
Beam Element ◽  
Large Displacements ◽  
Corotational Formulation ◽  
Geometric Nonlinearities ◽  
Small Strains ◽  
Number Of Layers ◽  
Von Karman ◽  
Interlayer Slip ◽  
Von Kármán

This paper presents a multilayered two node planar beam element, straight or shallow, of Bernoulli type, with an arbitrary number of layers with interlayer slip. Material and geometric nonlinearities are included. Small strains and slips are assumed. Large displacements are dealt with von Karman strain coupled with corotational formulation. No locking appears. Various tests show the capabilities of this element.

scholarly journals Supersonic Cascade Interaction

1974 ◽  
Author(s):  
H. J. Lichtfuss ◽  
H. Starken
Keyword(s):  
Exact Solution ◽  
Supersonic Flow ◽  
Flat Plate ◽  
Constant Velocity ◽  
Flow Conditions ◽  
Inlet Flow ◽  
Flow Adjustment ◽  
Outlet Flow ◽  
Quantitative Results ◽  
Cascade Interaction

The supersonic flow adjustment between two interacting blade rows is predicted theoretically. One of both cascades may have a constant velocity in the circumferential direction. The calculation is carried out in a quasi-stationary manner. This represents an exact solution if the constant inlet and outlet flow conditions are solely under the scope of view. Admitting the above assumptions it is possible to calculate the uniform outlet flow of the first and the associated inlet flow of the second cascade as a function of the circumferential velocity. Quantitative results are presented for flat plate cascades. However, the method is not at all restricted to these simple cases.

Piezoelectric beams under small strains but large displacements and rotations

2020 ◽  
Vol 87 ◽  
pp. 430-445
Author(s):  
A.L. Carvalho Neto ◽  
R.R.F. Santos ◽  
E. Lucena Neto ◽  
F.A.C. Monteiro
Keyword(s):  
Large Displacements ◽  
Small Strains

An Inverse Finite Element Strategy to Recover Full-Field, Large Displacements From Strain Measurements

2007 ◽  
Author(s):  
Krystian Paczkowski ◽  
H. R. Riggs
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Small Strain ◽  
Shell Structures ◽  
Small Displacement ◽  
Large Displacements ◽  
Full Field ◽  
Strain Measurements ◽  
Plate And Shell ◽  
Element Method

In active control of structures, it may be necessary to determine real-time displacements from measured deformations. Recently an inverse finite element method, iFEM, has been proposed to recover ‘small’ displacement fields for plate and shell structures from (small) strain measurements. A procedure to handle large displacements and nonlinear strains is presented in this paper. A similar least-squares error functional as in linear iFEM is used, but the linear strains are replaced with the Green-Lagrange strains, and a ‘total Lagrangian’ formulation is developed. As in the linear iFEM, the focus is again principally towards plate and shell structures. The functional is minimized with the finite element method. The nonlinear iFEM formulation is presented in detail and applied to a cantilever beam undergoing very large displacements. The relatively simple example is used to explore the formulation’s performance to recover large displacements. The results indicate that the approach is able to recover the large displacement field. Additional work is required to develop the method for practical application.

Estimating Over Temperature and its Duration in a Flat Plate With Sudden Changes in Heating and Cooling

2015 ◽  
Author(s):  
C.-S. Lee ◽  
T. I-P. Shih ◽  
K. M. Bryden
Keyword(s):  
Heat Transfer ◽  
Exact Solution ◽  
Steady State ◽  
Flat Plate ◽  
Time Lag ◽  
Convective Heating ◽  
Sudden Increase ◽  
Turbine Engine ◽  
Heating And Cooling ◽  
D Model

When the operating condition of a gas-turbine engine changes from one steady state to another, the cooling must ensure that the solid’s temperatures to never exceed the maximum allowable throughout the transient process. Exceeding the maximum allowable temperature is possible even though cooling is increased to compensate for the increase in heating because there is a time lag in how the solid responds to sudden changes in its convective heating and cooling environments. In this paper, a closed-form integral solution (referred to as the 1-D model) is generated to study the unsteady heat transfer in a flat plate subjected to sudden changes in convective heating and cooling. Comparison with the exact solution shows the 1-D model to be accurate within 0.1%. The 1-D model can be used to estimate the over temperature and its duration in a flat plate subjected to sudden changes in heating and cooling rates. For a given change in heating rate, the 1-D model can also be used to estimate the minimum cooling needed to ensure the new steady-state temperature will not exceed the maximum allowable. In addition, this model can estimate the precooled wall temperature needed before imposing a sudden increase in heat load to ensure no over temperature. This 1-D model was generalized for application to problems in multidimensions. The generalized model was used to estimate the duration of over temperature in a two-dimensional problem involving a step change in the heat-transfer coefficient on cooled side of a flat plate and provided results that match the exact solution within 5%.

Equilibrium Temperatures in a Boundary-Layer Flow Over a Flat Plate of Absorbing-Emitting Gas

1968 ◽  
Vol 90 (2) ◽  
pp. 257-266 ◽  
Author(s):  
Yehuda Taitel ◽  
J. P. Hartnett
Keyword(s):  
Boundary Layer ◽  
Exact Solution ◽  
Flat Plate ◽  
Interaction Mechanism ◽  
Approximate Solutions ◽  
Equilibrium Temperature ◽  
Constant Heat Flux ◽  
Adiabatic Wall ◽  
Approximate Methods ◽  
Layer Flow

The effect of radiation on the equilibrium temperature for a flow of emitting-absorbing gas over a flat plate is studied. Three methods of solution are formulated: An approximate solution for a thin boundary layer, a similarity solution for the limiting case when the boundary layer is optically thick, and an exact solution. Emphasis is put on the study of the recovery or adiabatic wall case, where conduction to the wall is balanced by the net radiation away from the wall. Results are reported for the limiting cases of a black plate and completely reflective plate and for a unit Prandtl number. The exact solution reflects very favorably on the use of the approximate methods and points out clearly the conditions for which the approximate solutions are applicable. Results are also reported for the equilibrium wall temperature for the case of constant heat flux and for the recovery factor in the case of blowing and suction; both for optically thin boundary layers. Special attention is put on the interaction mechanism and the role of the emitting-absorbing coefficient on this process. It is shown that, for small absorption coefficient, high wall emissivity, and Mach number, the results approach the case where the gas is transparent.

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