Large deflection analysis of plates stiffened by parallel beams

Sapountzakis, E. J.; Dikaros, I. C.

doi:10.1016/j.engstruct.2011.11.008

Cited by 9 publications

(4 citation statements)

References 35 publications

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“…Discretization of the integral representations of the displacement components and their derivatives with respect to , [49] and application to the domain nodal points yields…”

Section: For the Plate Displacement Componentsmentioning

confidence: 99%

“…Differentiating with respect to these functions, two and four times, respectively, yields 2 1 Equations (36a) and (36b) are quasi-static and indicate that the solution of (17a)-(17d) can be established by solving (36a) and (36b) under the same boundary conditions (equations (18)-(21b)) provided that the fictitious load distributions ( , ) ( = 1, 2, 3, 4) are first established. These distributions can be determined following the procedure presented in [49] and employing the constant element assumption for the load distributions along the internal beam elements (as the numerical implementation becomes very simple and the obtained results are of high accuracy). Thus, the integral representations of the displacement components ( = 1, 2, 3, 4) and their derivatives with respect to when applied to the beam ends (0, ), together with the boundary conditions (18)-(21b), are employed to express the unknown boundary quantities ( ), , ( ), , ( ), and , ( ) ( = 0, ) in terms of ( = 1, 2, 3, 4).…”

Section: For the Beam Displacement Components V And And For The Amentioning

confidence: 99%

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Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection

Dourakopoulos

Sapountzakis

2014

Advances in Civil Engineering

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In this paper a general solution to the geometrically nonlinear dynamic analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross-section, subjected to dynamic loading, is presented. The plate-beam structure is assumed to undergo moderate large deflections and the nonlinear analysis is carried out by retaining nonlinear terms in the kinematical relations. According to the proposed model, the arbitrarily placed parallel stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, making the hypothesis that the plate and the beams can slip in all directions of the connection without separation and taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting in two interface lines, along which the loading of the beams and the additional loading of the plate are defined. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM-based method. Both free and forced transverse vibrations are considered and numerical examples with great practical interest are presented demonstrating the effectiveness, wherever possible, the accuracy, and the range of applications of the proposed method.

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“…Discretization of the integral representations of the displacement components and their derivatives with respect to , [49] and application to the domain nodal points yields…”

Section: For the Plate Displacement Componentsmentioning

confidence: 99%

Section: For the Beam Displacement Components V And And For The Amentioning

confidence: 99%

Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection

Dourakopoulos

Sapountzakis

2014

Advances in Civil Engineering

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“…Plates are basic structural members which are used extensively in many disciplines like mechanical, civil, aerospace, and marine engineering, and in offshore structures. Because of their practical importance, the analysis of plates has always received significant interest, and thousands of studies have been published [1][2][3][4][5][6][7][8][9][10][11][12]. These studies may be categorized into various ways with regard to (i) the shape of the plate, (ii) the plate theory, (iii) the solution method, (iv) the material properties, (v) the boundary conditions, (vi) the scope of research (bending, buckling, or vibration), (vii) the type of analysis (theoretical, experimental or computational), and (viii) the classifications based on the thickness (membrane, thin, moderately thick or thick [13].…”

Section: Introductionmentioning

confidence: 99%

Bending of Super-Elliptical Mindlin Plates by Finite Element Method

Altekin

2018

Teknik Dergi

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Bending of shear deformable super-elliptical plates under transverse load was investigated using the Mindlin plate theory by means of the finite element method. Four-noded isoparametric quadrilateral plate bending element with three degrees of freedom per node was used. Parametric results for the maximum deflections were presented via sensitivity analysis for several geometric characteristics such as thickness, aspect ratio, and superelliptical power. Good agreement with the solutions of elliptical and rectangular plates was obtained using fine mesh. The results revealed that the deflections of clamped and point supported super-elliptical plates lie in the range bounded by elliptical and rectangular plates. However, the bending response of simply supported plates was observed to be entirely different. It was shown that high rate of convergence is required to obtain such a relation and using insufficient number of degrees of freedom results in finding a totally different trend for the clamped case.

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“…Hartmann and Zomantel [25], further developed the method, and implemented it for plate with relatively complex geometries and loadings. Following the above work, others (Tanaka and Miyazaki [62], Fernandes and Venturini [68], Paiva and Aliabadi [42], Albuquerque [2] among others [31,32,55,3,9,41,58,60,23,29,34,64,72]) have further extended the formulation for the classical plate.…”

Section: Introductionmentioning

confidence: 99%

Boundary element analysis of stiffened panels with repair patches

Pisa¹,

Aliabadi²

2015

Engineering Analysis with Boundary Elements

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In this paper a boundary element method for analysis of fractured stiffened panels repaired with riveted or adhesively bonded patches is presented. In order to achieve such a formulation, several boundary element formulations involving the membrane and bending of displacement, and, stress resultants are coupled together to analyse the model. The multi-region formulation is used to simulate the stiffeners, which are modelled as an assembly. They are then connected to the sheets to form the stiffened panels by means of a rivet formulation. The dual boundary element method is used to simulate the presence of cracks, and the patches, treated as independent plates, are joined to the panel either with rivets or adhesive. A boundary element formulation for adhesive bonding is implemented to model the adhesively bonded patches. The Crack Opening Displacements (COD) method and the Jintegral are implemented to evalute the required fracture parameters. Examples presented include a wing box with a three spar section, with fully stiffened skin, and, the skin is considered to have a crack and a repair patch is used on top of the crack to stop its growth.Response to Reviewers: Thank you for highlighting the missing references and figures numbers as well as certain typo's. We have corrected all the highlighted items.Thank you for highlighting the missing references and figures numbers as well as certain typo's. We have corrected all the highlighted items. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 Detailed Response to Reviewers AbstractIn this paper a boundary element method for analysis of fractured stiffened panels repaired with riveted or adhesively bonded patches is presented. In order to achieve such a formulation, several boundary element formulations involving the membrane and bending of displacement, and, stress resultants are coupled together to analyse the model. The multi-region formulation is used to simulate the stiffeners, which are modelled as an assembly. They are then connected to the sheets to form the stiffened panels by means of a rivet formulation. The dual boundary element method is used to simulate the presence of cracks, and the patches, treated as independent plates, are joined to the panel either with rivets or adhesive. A boundary element formulation for adhesive bonding is implemented to model the adhesively bonded patches. The Crack Opening Displacements (COD) method and the J-integral are implemented to evalute the required fracture parameters. Examples presented include a wing box with a three spar section, with fully stiffened skin, and, the skin is considered to have a crack and a repair patch is used on top of the crack to stop its growth.

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Large deflection analysis of plates stiffened by parallel beams

Cited by 9 publications

References 35 publications

Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection

Nonlinear Dynamic Analysis of Plates Stiffened by Parallel Beams with Deformable Connection

Bending of Super-Elliptical Mindlin Plates by Finite Element Method

Boundary element analysis of stiffened panels with repair patches

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