Optimally reinforced cutouts in laminated circular cylindrical shells

Şenocak, E.; Waas, Anthony M.

doi:10.1016/0020-7403(95)00046-z

Cited by 7 publications

(2 citation statements)

References 13 publications

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“…This fact implies that the presence of the inhomogeneity will alter the original stress resultant field in the infinite matrix. It has been observed that certain reinforced ''neutral'' holes may be designed for laminated plates and shells that do not alter the original stress distribution in the cut sheet [9][10][11][12]. Here we will address a similar issue by virtue of a circular inhomogeneity with a single interphase layer.…”

Section: Applicationmentioning

confidence: 99%

Multiphase circular inhomogeneities in isotropic laminated plates

Wang

2016

Mathematics and Mechanics of Solids

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This work is concerned with a circular inhomogeneity bonded to an infinite matrix though N concentric circular interphase layers within the context of Kirchhoff theory for isotropic laminated plates. An elegant and effective procedure is proposed to obtain the stress resultant fields within the internal inhomogeneity and the surrounding matrix under thermomechanical loadings. The boundary value problem is finally reduced to two coupled linear algebraic equations and four coupled linear algebraic equations that determine the six real coefficients of the stress resultant field in the inhomogeneity. In particular, the average stress resultants within the inhomogeneity can be directly determined from these six real coefficients. The other six unknown real coefficients, which control the stress resultant field in the surrounding matrix, can then be simply obtained. The effect of the N interphase layers on the stress resultant field is demonstrated by their influence on these 12 real coefficients. The obtained solution is further applied to the design of neutral and harmonic circular elastic inhomogeneities with a single interphase layer.

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Section: Applicationmentioning

confidence: 99%

Multiphase circular inhomogeneities in isotropic laminated plates

Wang

2016

Mathematics and Mechanics of Solids

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“…If the hole is to be neutral, giving rise to no variation in the prevailing stress field, reinforcement of varying sectional area is required as shown by Senocak and Waas (1995). If reinforcement is not a desirable option, then the inverse problem statement is to ask what cutout shape would give rise to the least perturbation in the stress field.…”

Section: Introductionmentioning

confidence: 98%

Shape optimization of interior cutouts in composite panels

Falzon

Steven

Xie

1996

Structural Optimization

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This paper presents validated results of the optimization of cutouts in laminated carbon-fibre composite panels by adapting a recently developed optimization procedure known as Evolutionary Structural Optimization (ESO). An initial small cutout was introduced into each finite element model and elements were removed from around this cutout based on a predefined rejection criterion. In the examples presented, the limiting ply within each plate element around the cutout was determined based on the Tsai-Hill failure index. Plates with values below the product of the average Tsai-Hill number and a rejection ratio (RR) were subsequently removed. This process was iterated until a steady state was reached and the RR was then incremented by an evolutionary rate (ER). The above steps were repeated until a cutout of a desired area was achieved. = stress in fibre direction = stress in transverse direction = shear stress = tensile/compressivestrength infibre direction = tensile/compressive strength in transverse direction = shear strength = plate element number lying on edge of cutout = plate element number = total number of plates = Tsai-Hill number = limiting Tsai-Hill number of plate e = limiting Tsai-Hill number of plate p = rejection ratio = global stiffness matrix = displacement vector = force vector = stress vector --ply number = number ofpliesper plate = failure index = specified condition on which to terminate evolution(e.g, areaof cutout) = stress at major vertexof ellipse = stress at minor vertex of ellipse = ellipse major axis = ellipse minor axis = increment number = evolutionary rate

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Stress–Strain State of Flexible Orthotropic Cylindrical Shells with a Reinforced Circular Hole

2015

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The stress-strain state of flexible orthotropic cylindrical shells with a reinforced circular hole under static loading is analyzed numerically. The incremental-loading procedure, modified Newton-Kantorovich method, and finite-element method are used. The effect of geometrical nonlinearity, the orthotropy of the material, and the stiffness of the reinforcement in a shell subject to uniform internal pressure on the distribution of stresses, strains, and displacements along the hole edge and in the zone of their concentration is studied Keywords: flexible orthotropic cylindrical shell, geometrical nonlinearity, stress concentration, reinforced circular hole, finite deflections, internal pressureIntroduction. Traditionally, a shell with a reinforced hole is considered as a structure that consists of the shell proper and a one-dimensional thin rod reinforcing it. The stress-strain state (SSS) of each of these components is described by an applied theory and has its peculiarities. Therefore, the development of a theory that describes the SSS of shells with reinforced holes involves difficulties associated with the necessity of describing the combined action of components with different dimensionality and satisfying the interface conditions [4,7]. Note that the same difficulties are encountered in studying the SSS of ribbed shells [3,6,12,17].Most results on stress concentration in isotropic and anisotropic shells with reinforced holes were obtained by solving linear elastic problems with analytic, variational, and numerical methods and are reviewed in [4,7,11,16].Much fewer studies are concerned with nonlinear boundary-value problems of stress concentration, but mainly for shells of revolution under an axisymmetric load [4, 10, 13].Very few publications report on solution of nonlinear two-dimensional problems for shells with reinforced holes. For example, the effect of plastic strains and finite deflections on the SSS of isotropic shells with a reinforced curved hole was analyzed in [7,20]. A nonclassical approach to the design of thin composite shells with reinforced curved holes that employs the same formulas for the shell and the reinforcement was proposed in [14], where some numerical results on the nonlinear deformation of a flexible orthotropic cylindrical shell with a reinforced circular hole under uniform internal pressure are presented.It is of considerable interest to study the effect of a reinforced hole on the stability of composite shells [9,18,19].In what follows, we will use the approach described in [14] to formulate geometrically nonlinear problems for thin orthotropic cylindrical shells with a reinforced circular hole, outline a numerical method for solving this class of problems, and study the effect of geometrical nonlinearity, the orthotropy of the material, and the stiffness of the reinforcement on the distribution of displacements, strains, and stresses in the zone of their concentration.1. Problem Formulation. Basic Nonlinear Equations. Consider a thin cylindrical shell of radius R and thicknes...

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Optimally reinforced cutouts in laminated circular cylindrical shells

Cited by 7 publications

References 13 publications

Multiphase circular inhomogeneities in isotropic laminated plates

Multiphase circular inhomogeneities in isotropic laminated plates

Shape optimization of interior cutouts in composite panels

Stress–Strain State of Flexible Orthotropic Cylindrical Shells with a Reinforced Circular Hole

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