On the distribution of stress in a thin plate elastically supported along two edges at loads beyond the stability limit
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An adaptive control algorithm with on-line system identification capability has been developed. One of the great advantages of this scheme is that an additional system identification mechanism such as an additional uncorrelated random signal generator as the source of system identification is not required. A time-varying plate-cavity system is used to demonstrate the control performance of this algorithm. The time-varying system consists of a stainless-steel plate which is bolted down on a rigid cavity opening where the cavity depth was changed with respect to time. For a given externally located harmonic sound excitation, the system identification and the control are simultaneously executed to minimize the transmitted sound in the cavity. The control performance of the algorithm is examined for two cases. First, all the water was drained, the external disturbance frequency is swept with 1 Hz/sec. The result shows an excellent frequency tracking capability with cavity internal sound suppression of 40 dB. For the second case, the water level is initially empty and then raised to 3/20 full in 60 seconds while the external sound excitation is fixed with a frequency. Hence, the cavity resonant frequency decreases and passes the external sound excitation frequency. The algorithm shows 40 dB transmitted noise suppression without compromising the system identification tracking capability.
This paper deals with the buckling of the stiffened plate under uni-axial compression. The direct integration of the governing differential equation is performed and the exact solution to the problem is obtained. As examples, a square plate with single stiffener, and a stiffened three-span, continuous plate are investigated, with special attention given to the influence of stiffener misplacement on the buckling load and mode shape of the plate. It is found that a small misplacement of the stiffeners from the nominal configuration may change the buckling mode from a global one to a highly localized one.
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Elastic stiffness tailoring of laminated composite panels by allowing the fibers to curve within the plane of the laminate is a relatively novel design concept that has been demonstrated to be both beneficial and practical. In particular, for structures with highly non-uniform stress states, such as the case of a flat panel with a central hole subjected to in-plane loading, the concept is likely to provide substantial improvements in load carrying capability. The objective of the present study is to determine the effectiveness of stiffness tailoring through the use of curvilinear fibers to reduce stress concentrations around the hole and improve the load carrying capability of panels with holes. In this study software was created that translates standard finite element models with traditional laminate definitions into ones that possess stacking sequences with curvilinear fiber paths that are directly manufacturable using an advanced tow placement machine. Preliminary designs for the manufacturing and testing phase were determined through rudimentary design studies for flat plates without holes under axial compression. These candidate designs were then analyzed using finite element models that accurately reflect the test conditions and geometries in order to select final designs for testing. A total of six large panels, measuring three feet by six feet, each of which are used to produce four specimens with or without holes, were fabricated and delivered to NASA for machining and testing.
An elastic half plane containing a crack and stiffened by a cover plate is discussed. The asymptotic nature of the stress state in the half plane around an end point of the stiffener to determine the likely orientation of a possible fracture initiation and growth was studied. The problem is formulated for an arbitrary oriented radial crack in a system of singular integral equations. For an internal crack and for an edge crack, the problem is solved and the stress intensity factors at the crack tips and the interface stress are calculated. A cracked half plane with two symmetrically located cover plates is also considered. It is concluded that the case of two stiffeners appears to be more severe than that of a single stiffener.
Hyperbolic equation for infinite elastic plate under impact loading - structural dynamics
Stress intensity factors of periodically spaced elastic cover plates bonded to elastic half plane, solving contact problem by Fredholm integral equation
Systems of equations defining bending occurring in finite isotropic elastic thin plate supported by rigid or yielding columns
Large elastic-plate deflection equations criticized for applicability and consistency
An initially stressed rectangular plate is subjected to a transverse, time dependent load. The initial stress field is constant and parallel to two of the plate edges. The transverse load is uniformly distributed over a rectangular area, the sides of which are parallel to the sides of the plate. The problem is formulated within the framework of classical, three-dimensional elasticity theory, and an exact solution is obtained in series form. The case of static stability under pre-stress is also considered.
Stability of elastic rectangular plate with rectangular hole and subjected to forced loading of outer edge
Von Karman equations in dimensionless and finite difference forms for deflections of elastic circular plate with central hole under load solved by iteration
A procedure for analyzing and designing elastically tailored composite laminates using the STAGS finite element solver has been presented. The methodology used to produce the elastic tailoring, namely computer-controlled steering of unidirectionally reinforced composite material tows, has been reduced to a handful of design parameters along with a selection of construction methods. The generality of the tow-steered ply definition provides the user a wide variety of options for laminate design, which can be automatically incorporated with any finite element model that is composed of STAGS shell elements. Furthermore, the variable stiffness parameterization is formulated so that manufacturability can be assessed during the design process, plus new ideas using tow steering concepts can be easily integrated within the general framework of the elastic tailoring definitions. Details for the necessary implementation of the tow-steering definitions within the STAGS hierarchy is provided, and the format of the ply definitions is discussed in detail to provide easy access to the elastic tailoring choices. Integration of the automated STAGS solver with laminate design software has been demonstrated, so that the large design space generated by the tow-steering options can be traversed effectively. Several design problems are presented which confirm the usefulness of the design tool as well as further establish the potential of tow-steered plies for laminate design.
The analytical solution of a finite circular plate on an elastic foundation centrally loaded by the rigid indenter is discussed. The procedure to use NASTRAN as a subroutine to iteratively converge to this solution numerically is described.
Fundamental solutions which automatically satisfy boundary conditions at the interfaces of an elastic plate perfectly bonded to two elastic halfspaces are implemented in a three-dimensional BEM for crack problems. The BEM features a new integration scheme for highly singular kernels. The capability is achieved through a part analytic and part numerical integration procedure, such that the analytic part of the integration is similar for all slip/opening variations. Part-through elliptic cracks in an elastic plate with traction-free surfaces are analyzed and the SIF values along the crack front are found to compare favorably with the numerical SIF results of Raju and Newman (1979).
A theoretical and experimental study is made to investigate the effect on plate vibrations of varying the stiffness of corner elastic point supports. A theoretical model is developed using a Rayleigh-Ritz analysis which approximates the plate mode shapes as products of free-free beam modes. The elastic point supports are modelled both as massless translational springs, and springs with tip masses. The tip masses are included to better represent the experimental supports. An experiment is constructed using the bending stiffness of horizontal beams to support a square plate at its four corners. The stiffness of these supports can be varied over such a range that the plate fundamental frequency is lowered to 40% of the rigid support frequency. The variation with support stiffness of the frequencies of the first eight plate modes is measured, and compared with the theoretical results. The plate mode shapes for rigid supports are analyzed using holographic interferometry. There is excellent agreement between the theoretical and experimental results, except for high plate modes where the theoretical model is demonstrated to be inadequate.