Free-corner Effects in Cross-ply Laminates: An Approximate Higher-order                Theory Solution

Mittelstedt, Christian; Becker, Wilfried

doi:10.1177/0021998303036265

Cited by 17 publications

(15 citation statements)

References 71 publications

(82 reference statements)

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“…Thereinto, the meshes have been refined at the location x = 4 mm within the range 0 < y < 6 mm. Again, it can be found that the peak stress near free edge calculated from analytical approach [24,26] is less than the present results. …”

Section: Numerical Examplescontrasting

confidence: 78%

“…Subsequently, Becker et al [25] adopted an equilibrium stress distribution in conjunction with the principle of minimum complementary energy to describe the free-corner effects of cross-ply laminated plates. In addition, Mittelstedt and Becker [26,27] further developed the approximate higher-order theory to analyze the free-corner problems of laminated plates subjected to thermal loading.…”

Section: Introductionmentioning

confidence: 99%

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A higher-order displacement model for stress concentration problems in general lamination configurations

Wanji

2009

Materials & Design

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Section: Numerical Examplescontrasting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

A higher-order displacement model for stress concentration problems in general lamination configurations

Wanji

2009

Materials & Design

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“…In order to improve this methodology, Becker (2003a, 2004b) used an upgraded inplane stress field for laminates with arbitrary nonorthotropic layups. Mittelstedt and Becker (2003b) introduced a simple displacement based approach for pure rectangular cross-ply layups under thermal load by using a higher order single layer theory with trigonometric terms through the complete laminate thickness. Furthermore, Mittelstedt and Becker (2004c,d) employed a layerwise displacement based approach which applies a discretization of symmetric laminates with isotropic layers and cross-ply plates into an arbitrary number of mathematical layers through the plate thickness.…”

Section: Introductionmentioning

confidence: 99%

Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

Mittelstedt

Becker

2006

International Journal of Solids and Structures

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The Boundary Finite Element Method (BFEM), a novel semi-analytical boundary element procedure solely relying on standard finite element formulations, is employed for the investigation of the orders and modes of three-dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates. After a comprehensive literature review and a concise introduction to the standard three-dimensional BFEM formulation for the static analysis of general unbounded structures, we demonstrate the application of the BFEM for the computation of the orders and modes of two-dimensional and three-dimensional stress singularities for several classes of problems within the framework of linear elasticity. Special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates. In all cases, the BFEM computations agree excellently with available reference results. The required computational effort is found to be considerably lower compared to e.g. standard Finite Element Method (FEM) computations. In the case of free laminate corners, numerous new results on the occurring stress singularities are presented. It is found that free-corner problems generally seem to involve a more pronounced criticality than the corresponding free-edge situations.

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“…displacement-based equivalent single layer theory with trigonometric thickness terms and an exponential approach has been applied in [9]. Some investigations on the arising corner singularities are also available [10À12].…”

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confidence: 99%

“…This can be readily explained by the idea of two free-edge effects that interact in the closer corner regions and culminate to some kind of free-corner effect. In fact, the state of stress in the vicinity of free laminate corners is also of a distinct three-dimensional nature and exhibits steep stress gradients that are dominated by a mathematical singularity at the free laminate edges and especially at the free corner [6À12], even though the simple superposition of two freeedge effects to simulate the free-corner problem may lead to false results [8] and in fact is a simplification of the actual situation, which should only be applied for rectangular crossply laminates [8,9]. Nevertheless, even though free laminate corners seem to be an important technical situation as well as the classical free-edge effect in a tensile coupon, there are few investigations available concerning free-corner stress concentrations.…”

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confidence: 99%

A Variational Finite Layer Technique for the Investigation of Thermally Induced Stress Concentrations in Composite Structures

Mittelstedt¹,

Becker

2004

Journal of Thermal Stresses

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The technical relevance of stress fields near free laminate edges under mechanical and=or hygrothermal loads (''free-edge effect'') has long been recognized. However, the state of stress near free laminate corners (i.e., at corners that are generated by two merging straight free laminate edges) has gone nearly unnoticed in the open literature. To gain further insight into the mechanics of free-corner stress fields (''free-corner effect''), the present contribution is devoted to the closed-form analysis of displacements, strains and stresses in the vicinity of free rectangular corners of symmetric crossply laminates under uniform thermal load by means of a layerwise C 0 -continuous displacement approach. The laminate is discretized into an arbitrary number of mathematical layers through the thickness. However, concerning the two in-plane directions, no discretization is employed, but on the contrary, unknown in-plane functions are assumed that are then determined by application of the principle of minimum potential energy of the laminate. Due to some simplifying prerequisite assumptions concerning the utilized displacement approach and performing a separation of the in-plane variables, the resultant governing EulerÀLagrange equations are ordinary second-order differential equations that can be solved in a closedÀform way. Hence, all state variables of the given thermoelastic free-corner problem can be written in a closed-form manner, which makes the present method easily applicable and allows a good insight into the underlying mechanics. Given boundary conditions of traction-free laminate edges are satisfied in an average sense. The present method is easily applicable, requires little computational effort, and is in excellent conformity with accompanying finite element computations. Because the presented approach enables a closed-form analytic formulation with respect to the in-plane coordinates, it is appropriate to designate the methodology as a finite layer technique.The most common analysis tool for the determination of the mechanical behavior of composite laminates is the so-called classical laminate plate theory (CLPT; see, e.g., [1]). Being in essence a two-dimensional theory, CLPT assumes a plane state of stress in conjunction with the kinematical assumptions of Kirchhoff's classical plate theory and yields reasonably accurate results for the overall response of layered structures like in-plane stresses or buckling and free-vibration modes. However, in the vicinity of free edges of the laminate (e.g., in the presence of discontinuities like interfaces between dissimilar layers within composite laminates), the CLPT state of stress is heavily perturbed. In such areas, the assumptions of CLPT break down and threedimensional stress fields with steep gradients occur. Besides the in-plane stresses, interlaminar or out-of-plane stress components play an important role as well. This phenomenon is most commonly called free-edge effect and involves stress fields that on a theoretical basis are dominated by a mathema...

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Free-corner Effects in Cross-ply Laminates: An Approximate Higher-order Theory Solution

Cited by 17 publications

References 71 publications

A higher-order displacement model for stress concentration problems in general lamination configurations

A higher-order displacement model for stress concentration problems in general lamination configurations

Efficient computation of order and mode of three-dimensional stress singularities in linear elasticity by the boundary finite element method

A Variational Finite Layer Technique for the Investigation of Thermally Induced Stress Concentrations in Composite Structures

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