Non-linear analysis of plates by the Analog Equation Method

Katsikadelis, John T.; Nerantzaki, M. S.

doi:10.1007/bf00350282

Cited by 32 publications

(19 citation statements)

References 12 publications

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“…The FEM has been developed to solve nonlinear membrane problems (Leonard, 1988). With the exception of a D/BEM developed by Katsikadelis and Nerantzaki (1996), publications on the application of BEM to the problem at hand do not exist. In this paper a boundary-only BEM is developed for nonlinear analysis of membranes.…”

Section: Introductionmentioning

confidence: 93%

The analog equation method for large deflection analysis of membranes. A boundary-only solution

Katsikadelis

Nerantzaki

Tsiatas

2001

Computational Mechanics

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In this paper the analog equation method (AEM) is applied to nonlinear analysis of elastic membranes with arbitrary shape. In this case the transverse de¯ections inuence the inplane stress resultants and the three partial differential equations governing the response of the membrane are coupled and nonlinear. The present formulation, being in terms of the three displacements components, permits the application of geometrical inplane boundary conditions. The membrane is prestressed either by prescribed boundary displacements or by tractions. Using the concept of the analog equation the three coupled nonlinear equations are replaced by three uncoupled Poisson's equations with ®ctitious sources under the same boundary conditions. Subsequently, the ®ctitious sources are established using a procedure based on BEM and the displacement components as well as the stress resultants are evaluated from their integral representations at any point of the membrane. Several membranes are analyzed which illustrate the method and demonstrate its ef®ciency and accuracy. Moreover, useful conclusions are drawn for the nonlinear response of the membranes. The method has all the advantages of the pure BEM, since the discretization and integration is limited only to the boundary.

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Section: Introductionmentioning

confidence: 93%

The analog equation method for large deflection analysis of membranes. A boundary-only solution

Katsikadelis

Nerantzaki

Tsiatas

2001

Computational Mechanics

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“…The AEM for the plate equation including inplane forces has been developed by Katsikadelis and Nerantzaki [35]. According to this formulation, if w p is the sought solution of the boundary value problem described by Equations (1) and (2a, b), application of the biharmonic operator to this function yields…”

Section: For the Plate Transverse Deflection W Pmentioning

confidence: 99%

Analysis of plates stiffened by parallel beams

Sapountzakis

Mokos

2006

Numerical Meth Engineering

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SUMMARYIn this paper a general solution for the analysis of plates stiffened by parallel beams subjected to an arbitrary loading is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. The aforementioned integrated tractions result in the loading of the beams as well as the additional loading of the plate. Their distribution is established by applying continuity conditions in all directions at the interfaces. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. Six boundary value problems with respect to the plate transverse deflection, to the plate inplane displacement components, to the beam transverse deflections, to the beam axial deformation and to the beam non-uniform angle of twist are formulated and solved using the analog equation method (AEM), a boundary element method (BEM)-based method employing a boundary integral equation approach. The solution of the aforementioned plate and beam problems, which are non-linearly coupled, is achieved using iterative numerical methods. The adopted model describes better the actual response of the plate beams system and permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. The evaluated lateral deflections of the plate-beams system are found to exhibit considerable discrepancy from those of other models, which neglect inplane and axial forces and deformations.

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“…(1), (6a, b), (8), (11) are solved using the Analog Equation Method (AEM) (Katsikadelis 1994, Katsikadelis & Nerantzaki 1994 as follows.…”

Section: Solution Proceduresmentioning

confidence: 99%

Dynamic analysis of elastic plates reinforced with beams of doubly-symmetrical cross section

Sapountzakis

Katsikadelis

1999

Computational Mechanics

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In this paper a solution to the dynamic problem of elastic plates reinforced with beams of doubly ± symmetrical cross section is presented. The adopted model takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The method of analysis is based on the capability to establish a¯exibility matrix with respect to a set of nodal mass points using the Analog Equation Method (AEM) for the static plate problem. A lumped mass matrix is constructed from the tributary mass areas to the nodal mass points. Both free and forced transverse vibrations are considered and numerical examples with great practical interest are presented. The discrepancy in the obtained eigenfrequencies using the presented analysis, which approximates better the actual response of the plate-beams system, and the corresponding ones ignoring the inplane forces and deformations justify the analysis based on the proposed model.

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Non-linear analysis of plates by the Analog Equation Method

Cited by 32 publications

References 12 publications

The analog equation method for large deflection analysis of membranes. A boundary-only solution

The analog equation method for large deflection analysis of membranes. A boundary-only solution

Analysis of plates stiffened by parallel beams

Dynamic analysis of elastic plates reinforced with beams of doubly-symmetrical cross section

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