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At least 73 records · Page 4

Reciprocal relations for transmission coefficients - Theory and application

The authors present a rigorous proof of certain intuitively plausible reciprocal relations for time harmonic plane-wave transmission and reflection at the interface between a fluid and an anisotropic elastic solid. Precise forms of the reciprocity relations for the transmission coefficients and for the transmitted energy fluxes are derived, based on the reciprocity theorem of elastodynamics. It is shown that the reciprocity relations can be used in conjunction with measured values of peak amplitudes for transmission through a slab of the solid (water-solid-water) to obtain the water-solid coefficients. Experiments were performed for a slab of a unidirectional fiber-reinforced composite. Good agreement of the experimentally measured transmission coefficients with theoretical values was obtained.

Qu, Jianmin↗

Open-mode delamination stress concentrations in horseshoe and elliptic composite curved bars subjected to end forces

The multilayer theory of anisotropic elasticity and a finite element method were used to analyze the open-mode delamination stress concentrations in horseshoe and elliptic laminated composite curved bars. Two types of laminations, solid laminations and sandwich laminations, were analyzed. It was found that the open-mode delamination stress concentration could be greatly increased in these two types of curved bars by decreasing their aspect ratios. The open-mode delamination stress concentration generated in the solid laminations was found to be far more severe than that generated in the sandwich laminations. The horseshoe curved bar may be used to determine both the open-mode delamination strength of solidly laminated composites and the open-mode debonding strength of sandwiched laminated composites. However, the elliptic curved bar is only good for determining the open-mode delamination strength of solidly laminated composites.

Ko, William L.↗

Analyses of composite fuselage structure under various loading conditions

With the characteristics of high strength/weight and stiffness/weight ratios in advanced composite materials, composite plate structures have been successfully applied to secondary load-carrying structural components in the aerospace industry for the past two decades. Recently, filament wound composite shells are being considered for design of primary fuselage structures. To implement the design the structural response under various loading conditions needs to be predicted accurately. Therefore, it is essential to establish a rigorous analytical solution in the area of composite laminated shells. A closed form solution is presented that predicts the response of a composite shell subjected to internal pressure, axial tension, bending, and torsion. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity coupled partial differential governing equations are developed using Lehknitskii's stress function approach. The general expressions for the stresses and displacements in the composite cylinders under these loading conditions is discussed. Three examples (45) off-axis unidirectional, (45/45) unsymmetric, and (45/45)(sub s) symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratios, coupling, and stacking sequence.

Yuan, Fuh-Gwo↗

Analysis of laminated composite shells under internal pressure

A closed form solution is presented that predicts the response of filament wound composite shells subjected to internal pressure. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity coupled differential equations are developed using Lekhnitskii's stress function approach. Two composite systems, graphite/epoxy and glass/epoxy, are selected to demonstrate the influence of degree of material anisotropy and fiber orientations on the axial and induced twisting deformation. Detailed stress distributions of (45) off-axis unidirectional and (45/-45)s symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratio and stacking sequence.

Yuan, F. G.↗

Deformation and stress response of composite laminated shells under internal pressure

This paper presents a theoretical study of the response of filament wound composite shells under internal pressure. Each layer of the material is generally cylindrically anisotropic. By using cylindrically anisotropic elasticity field equations and Lekhnitskii's stress functions, a system of sixth-order ordinary differential equations is obtained. The general expressions for the stresses and displacements in the laminated composite shells under internal pressure are discussed. Two composite systems, graphite/epoxy and glass/epoxy, are selected to demonstrate the influence of degree of material anisotropy and fiber orientations on the axial and induced twisting deformation. Stress distributions of (45/-45)s symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratio.

Yuan, F. G.↗

Free-edge effects in laminates under extension, bending and twisting. II - Sublaminate/layer modeling and analysis

The stress-function-based variational method of Yin (1991) is extended and modified into a combined layer/sublaminate approach applicable to a laminated strip composed of a large number of differently orientated, anisotropic elastic plies. Lekhnitskii's (1963) stress functions are introduced into two interior layers adjacent to a particular interface. The remaining layers are grouped into an upper sublaminate and a lower sublaminate. The stress functions are expanded in truncated power series of the thickness coordinate, and the differential equations governing the coefficient functions are derived by using the complementary virtual work principle. The layer/sublaminate approach limits the dimension of the eigenvalue problem to a fixed number irrespective of the number of layers in the sublaminate, so that reasonably accurate solutions of the interlaminar stresses can be computed with extreme ease. For symmetric, four-layer, angle-ply and cross-ply laminates, a comparison of the previous analysis results based on the pure layer model and new results based on two different layer/sublaminate models indicates reasonable over-all agreement in the interlaminar stresses and superior agreement in the total peeling and shearing force.

Yin, Wan-Lee↗

Composite laminated shells under internal pressure

A theoretical study is conducted of the response of filament-wound composite shells under internal pressure; a system of sixth-order ordinary differential equations is obtained by means of the cylindrically anisotropic elasticity field equations and Lekhnitskii's (1963) stress functions. The general expressions for the stresses and displacements in the laminated composite shells under internal pressure are discussed. Attention is given to the influence of the degree of material anisotropy and fiber orientation on the axial and induced twisting deformation.

Yuan, F. G.↗

Secondary orientation effects in a single crystal superalloy under mechanical and thermal loads

The nickel-base single crystal superalloy PWA 1480 is a candidate blading material for the advanced turbopump development program of the SSME. In order to improve thermal fatigue resistance of the turbine blades, the single crystal superalloy PWA 1480 is grown along the low modulus zone axes (001) crystal orientation by a directional solidification process. Since cubic single crystal materials such as PWA 1480 exhibit anisotropic elastic behavior, the stresses developed within the single crystal superalloy due to mechanical and thermal loads are likely to be affected by the exact orientation of the secondary crystallographic direction with respect to the geometry of the turbine blade. The effects of secondary crystal orientation on the elastic response of single crystal PWA 1480 superalloy were investigated.

Kalluri, Sreeramesh↗

A displacement gradient BEM for accurate stress computation near boundaries in 2-D anisotropic problems

A displacement gradient method for 2D anisotropic elasticity problems is presented, which effectively minimizes the boundary layer effect through a two-step procedure. First, the boundary integral equations are solved for the unknown boundary displacements and tractions. Second, a direct integral equation for displacement gradients is developed in terms of boundary tractions. Three methods based on different evaluation procedures and locations for determining the displacement gradients are proposed. In the first method the displacement gradients are averaged at nodes common to adjacent elements. The second method stores the gradients element-wise. In the third method, the gradients are evaluated at the nodes of discontinuous elements. The three methods are applied to near-isotropic plates with circular and elliptic cutouts. It is concluded that all three methods can yield accurate stress distributions.

Sistla, R.↗

Thickness and orientational design for a maximum stiff membrane

Recent results from sensitivity analysis for strain energy with anisotropic elasticity are applied to thickness and orientational design of laminated membranes. Primarily, the first order gradients of the total elastic energy are used in an optimality criteria based method. This traditional method is shown to give slow convergence with respect to design parameters, although the convergence of strain energy is very good. To get a deeper insight into this rather general characteristic, second order derivatives are included and it is shown how they can be obtained by first order sensitivity analysis. Examples of only thickness design, only orientational design, and combined thickness--orientational design are presented.

Pedersen, Pauli↗

Structure and stability of hydrous minerals at high pressure

The presence of even small amounts of hydrogen in the Earth's deep interior may have profound effects on mantle melting, rheology, and electrical conductivity. The recent discovery of a large class of high-pressure H-bearing silicates further underscores the potentially important role for hydrous minerals in the Earth's mantle. Hydrogen may also be a significant component of the Earth's core, as has been recently documented by studies of iron hydride at high pressure. In this study, we explore the role of H in crystal structures at high pressure through detailed Raman spectroscopic and x ray diffraction studies of hydrous minerals compressed in diamond anvil cells. Brucite, Mg(OH)2, has a simple structure and serves as an analogue for the more complex hydrous silicates. Over the past five years, this material has been studied at high pressure using shock-compression, powder x ray diffraction, infrared spectroscopy, Raman spectroscopy, and neutron diffraction. In addition, we have recently carried out single-crystal synchrotron x-ray diffraction on Mg(OH)2 and Raman spectroscopy on Mg(OD)2 at elevated pressure. From all these studies, an interesting picture of the crystal chemical behavior of this material at high pressure is beginning to emerge. Some of the primary conclusions are as follows: First, hydrogen bonding is enhanced by the application of pressure. Second, layered minerals which are elastically anisotropic at low pressure may not be so at high pressure. Furthermore, the brucite data place constraints on the effect of hydrogen on seismic velocities and density at very high pressure. Third, the stability of hydrous minerals may be enhanced at high P by subtle structural rearrangements that are difficult to detect using traditional probes and require detailed spectroscopic analyses. Finally, brucite appears to be unique in that it undergoes pressure-induced disordering that is confined solely to the H-containing layers of the structure.

Duffy, T. S.↗

Calculation of Stress Intensity Factors for Interfacial Cracks in Fiber Metal Laminates

Stress intensity factors for interfacial cracks in Fiber Metal Laminates (FML) are computed by using the displacement ratio method recently developed by Sun and Qian (1997, Int. J. Solids. Struct. 34, 2595-2609). Various FML configurations with single and multiple delaminations subjected to different loading conditions are investigated. The displacement ratio method requires the total energy release rate, bimaterial parameters, and relative crack surface displacements as input. Details of generating the energy release rates, defining bimaterial parameters with anisotropic elasticity, and selecting proper crack surface locations for obtaining relative crack surface displacements are discussed in the paper. Even though the individual energy release rates are nonconvergent, mesh-size-independent stress intensity factors can be obtained. This study also finds that the selection of reference length can affect the magnitudes and the mode mixity angles of the stress intensity factors; thus, it is important to report the reference length used with the calculated stress intensity factors.

Wang, John T.↗

Integrated Structural/Acoustic Modeling of Heterogeneous Panels

A model for the dynamic response of heterogeneous media is presented. A given medium is discretized into a number of subvolumes, each of which may contain an elastic anisotropic material, void, or fluid, and time-dependent boundary conditions are applied to simulate impact or incident pressure waves. The full time-dependent displacement and stress response throughout the medium is then determined via an explicit solution procedure. The model is applied to simulate the coupled structural/acoustic response of foam core sandwich panels as well as aluminum panels with foam inserts. Emphasis is placed on the acoustic absorption performance of the panels versus weight and the effects of the arrangement of the materials and incident wave frequency.

Bednarcyk, Brett, A.↗

On the Buckling of Imperfect Anisotropic Shells with Elastic Edge Supports Under Combined Loading Part I:: Theory and Numerical Analysis - Pt. 1

A rigorous solution is presented for the case of stiffened anisotropic cylindrical shells with general imperfections under combined loading, where the edge supports are provided by symmetrical or unsymmetrical elastic rings. The circumferential dependence is eliminated by a truncated Fourier series. The resulting nonlinear 2-point boundary value problem is solved numerically via the "Parallel Shooting Method". The changing deformation patterns resulting from the different degrees of interaction between the given initial imperfections and the specified end rings are displayed. Recommendations are made as to the minimum ring stiffnesses required for optimal load carrying configurations.

Arbocz, Johann↗

A mixed-mode crack analysis of rectilinear anisotropic solids using conservation laws of elasticity

A very simple and convenient method of analysis for studying two-dimensional mixed-mode crack problems in rectilinear anisotropic solids is presented. The analysis is formulated on the basis of conservation laws of anisotropic elasticity and of fundamental relationships in anisotropic fracture mechanics. The problem is reduced to a system of linear algebraic equations in mixed-mode stress intensity factors. One of the salient features of the present approach is that it can determine directly the mixed-mode stress intensity solutions from the conservation integrals evaluated along a path removed from the crack-tip region without the need of solving the corresponding complex near-field boundary value problem. Several examples with solutions available in the literature are solved to ensure the accuracy of the current analysis. This method is further demonstrated to be superior to other approaches in its numerical simplicity and computational efficiency. Solutions of more complicated and practical engineering problems dealing with the crack emanating from a circular hole in composites are presented also to illustrate the capacity of this method.

Wang, S. S.↗

Free-Edge Failures of Composite Laminates

The free-edge delamination of graphite/epoxy laminates under static loading is being analyzed to obtain fundamental understanding of the continuum mechanics involved. The analyses are conducted by idealizing the material response of each ply in the laminate as homogenous, linear elastic, and anisotropic. A generalized plane strain elastic boundary value problem was formulated to investigate the energy variation of such a body.

Source record↗

Buckling Behavior of Long Anisotropic Plates Subjected to Elastically Restrained Thermal Expansion

An approach for synthesizing buckling results for, and behavior of, thin balanced and unbalanced symmetric laminates that are subjected to uniform heating or cooling and elastically restrained against thermal expansion or contraction is presented. This approach uses a nondimensional analysis for infinitely long, flexurally anisotropic plates that are subjected to combined mechanical loads and is based on useful nondimensional parameters. In addition, stiffness-weighted laminate thermal-expansion parameters and compliance coefficients are derived that are used to determine critical temperatures in terms of physically intuitive mechanical-buckling coefficients. The effects of membrane orthotropy and membrane anisotropy are included in the general formulation. Many results are presented for some common laminates that are intended to facilitate a structural designer's transition to the use of generic buckling design curves. Several curves that illustrate the fundamental parameters used in the analysis are presented, for nine contemporary material systems, that provide physical insight into the buckling response in addition to providing useful design data. Examples are presented that demonstrate the use of generic design curves. The analysis approach and generic results indicate the effects and characteristics of elastically restrained laminate thermal expansion or contraction, membrane orthotropy and anisotropy, and flexural orthotropy and anisotropy in a very general and unifying manner.

Nemeth, Michael P.↗