Showing papers on "Orthotropic material published in 1991"
TL;DR: In this paper, an exact analytical treatment of the interaction of harmonic elastic waves with n-layered anisotropic plates is presented, where the wave is allowed to propagate along an arbitrary angle from the normal to the plate as well as along any azimuthal angle.
Abstract: Exact analytical treatment of the interaction of harmonic elastic waves with n-layered anisotropic plates is presented. Each layer of the plate can possess up to as low as monoclinic symmetry and thus allowing results for higher symmetry materials such as orthotropic, transversely isotropic, cubic, and isotropic to be obtained as special cases. The wave is allowed to propagate along an arbitrary angle from the normal to the plate as well as along any azimuthal angle. Solutions are obtained by using the transfer matrix method. According to this method formal solutions for each layer are derived and expressed in terms of wave amplitudes. By eliminating these amplitudes the stresses and displacements on one side of the layer are related to those of the other side. By satisfying appropriate continuity conditions at interlayer interfaces a global transfer matrix can be constructed which relates the displacements and stresses on one side of the plate to those on the other. Invoking appropriate boundary conditions on the plates outer boundaries a large variety of important problems can be solved. Of these mention is made of the propagation of free waves on the plate and the propagation of waves in a periodic media consisting of a periodic repetition of the plate. Confidence is the approach and results are confirmed by comparisons with whatever is available from specialized solutions. A variety of numerical illustrations are included.
335 citations
TL;DR: In this article, the boundary value problem is reduced to a set of coupled ordinary differential equations and then solved by the method of Frobenius by assuming suitable displacement functions, and the results are shown to give results identical to those of a stress function approach for a plane strain problem.
195 citations
TL;DR: In this paper, a higher-order plate theory is used in each individual layer to determine the natural frequencies and the relative stress and deflection distributions through the thickness of simply supported rectangular plates.
193 citations
TL;DR: In this article, a spatial rescaling has been used to reduce the orthotropic problems to equivalent problems in materials with cubic symmetry, and solutions for orthotropic materials can be constructed approximately from isotropic material solutions or rigorously from cubic ones.
187 citations
TL;DR: Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined in this article, where the authors extend an established framework for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response.
Abstract: Singular fields around a crack running dynamically along the interface between two anisotropic substrates are examined Emphasis is placed on extending an established framework for interface fracture mechanics to include rapidly applied loads, fast crack propagation and strain rate dependent material response For a crack running at non-uniform speed, the crack tip behaviour is governed by an instantaneous steady-state, two-dimensional singularity This simplifies the problem, rendering the Stroh techniques applicable In general, the singularity oscillates, similar to quasistatic cracks The oscillation index is infinite when the crack runs at the Rayleigh wave speed of the more compliant material, suggesting a large contact zone may exist behind the crack tip at high speeds In contrast to a crack in homogeneous materials, an interface crack has a finite energy factor at the lower Rayleigh wave speed Singular fields are presented for isotropic bimaterials, so are the key quantities for orthotropic bimaterials Implications on crack branching and substrate cracking are discussed Dynamic stress intensity factors for anisotropic bimaterials are solved for several basic steady state configurations, including the Yoffe, Gol'dshtein and Dugdale problems Under time-independent loading, the dynamic stress intensity factor can be factorized into its equilibrium counterpart and the universal functions of crack speed
169 citations
TL;DR: In this article, the accuracy and convergence of the method of differential quadrature for solving a variety of differential equations with variable coefficients associated with plate and beam instability problems were discussed.
155 citations
TL;DR: In this article, an efficient stiffness optimization approach on orthotropic laminated composites using lamination parameters is presented, where the stiffness components are expressed as a linear function of lamin parameters in the classical lamination theory.
Abstract: The paper presents an efficient stiffness optimization approach on orthotropic laminated composites using lamination parameters. It is efficient to use lamination parameters as design variables since the stiffness components of laminated composites are expressed as a linear function of lamination parameters in the classical lamination theory. As an example of stiffness optimizations, the buckling optimization of orthotropic laminated cylindrical shells under combined loadings is treated using a mathematical programming method. The present approach shows good convergence behaviors for the optimum design and gives reliable optimization results.
141 citations
TL;DR: In this paper, sensitivity analysis for strain energy with anisotropic elasticity is applied to thickness and orientational design of laminated membranes, and the first order gradients of the total elastic energy are primarily used in an optimality criteria based method.
Abstract: Recent results from sensitivity analysis for strain energy with anisotropic elasticity are applied to thickness and orientational design of laminated membranes. The first order gradients of the total elastic energy are primarily 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 gain 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 thickness design only, orientational design only and combined thickness-orientational design are presented.
138 citations
TL;DR: In this article, sound transmission loss characteristics of panel constructions with thin face sheets and a thicker, lighter core are investigated, and the occurrence of acoustic coincidence is described for symmetric and antisymmetric modes of propagation, in the panel.
Abstract: The sound transmission loss (TL) characteristics of panel constructions with thin face sheets and a thicker, lighter core are investigated. Analytical models of TL are developed for constructions with isotropic and orthotropic core materials. The occurrence of acoustic coincidence is described for symmetric and antisymmetric modes of propagation, in the panel. Symmetric propagation involves thickness deformation of the core, while antisymmetric propagation involves a bending deformation of the panel without thickness deformation. For symmetric modes, coincidence occurs near the conventional double wall resonance frequency characterized by the stiffness of the core and the mass of the face sheets, and also at higher frequencies associated with bending wave propagation in the face sheets. Antisymmetric modes account for shear deformation in the core, which results in a softening of the bending rigidity of the panel at higher frequencies. For orthotropic core materials, the acoustic behavior is dependent on ...
126 citations
TL;DR: In this paper, an elegant procedure is proposed for obtaining components of the orthotropic or anisotropic in-plane permeability tensor from experimental data on flow front position and time.
Abstract: An elegant procedure is proposed for obtaining components of the orthotropic or anisotropic in-plane permeability tensor from experimental data on flow front position and time. A radial flow geometry allows the shape of the advancing flow front to be dictated by the in-plane permeability of the fabric media. The directional permeabilities in the fabric plane are directly calculated from fluid and fabric properties together with data from the mold filling experiment (resin injection pressure and flow front position with time). The simplicity of the apparatus and proposed analytical procedure permit easy testing and comparison of different types of fibrous media.
121 citations
TL;DR: In this paper, the stability of cylindrical shells under axial compression, external pressure, and/or torsion possessing general nonsymmetric random initial imperfections can be evaluated.
Abstract: Using the first-order, second-moment analysis, a stochastic method is presented, whereby the stability of isotropic, orthotropic, and anisotropic nominally circular cylindrical shells under axial compression, external pressure, and/or torsion possessing general nonsymmetric random initial imperfections can be evaluated
TL;DR: VICONOPT as mentioned in this paper is a 23,000 line Fortran 77 computer program that incorporates the earlier programs VIPASA2 and VICON, which covers prismatic assemblies of anisotropic plates exactly for buckling and vibration analysis and also for design subject to buckling constraints.
Abstract: ASUMMARY is given of key features of the computer program VICONOPT,1 which covers prismatic assemblies of anisotropic plates exactly for buckling and vibration analysis and also for design subject to buckling constraints. Contents VICONOPT (VIpasa with CONstraints and OPTimization) is a 23,000 line Fortran 77 computer program that incorporates the earlier programs VIPASA2 and VICON.3 It covers any prismatic assembly of anisotropic plates and Fig. 1 shows typical cross sections. Each plate can carry any combination of NL, NT9 and Ns, the longitudinally invariant in-plane forces per unit length of plate edge shown in Fig. 1. VICONOPT performs analysis or optimum design. The analysis includes calculation of critical buckling load factors, or undamped natural frequencies, and mode shapes. VIPASA uses the stiffness matrix method based on exact flat plate theory with Winkler foundations. It also uses an algorithm that guarantees convergence on all required eigenvalues and permits the user to employ nested (to any level) substructuring very concisely and flexibly to reduce solution times, data preparation, and computer memory usage. The mode of buckling or vibration is assumed to vary sinusoidally in the longitudinal direction x> with the displacement amplitudes u, v, w, and ^ shown in Fig. 1 and with computations being repeated for a user specified set of half-waveleng ths X. Plate bending and membrane behaviors are uncoupled and the bending and in-plane stiffness matrices D and A are respectively fully populated and orthotropic, which treats balanced symmetric laminates. The global stiffness matrix becomes complex when anisotropy or shear loading are present, thus, increasing solution time. The nodal lines of zero displacement are straight and in the y direction if all plates are orthotropic with Ns = 0, and so satisfy simply supported end conditions. Otherwise, solutions only approximate such end conditions and become excessively conservative as A approaches L Dead load values of NL, NT9 and Ns are permitted for both buckling and vibration problems. In the former case they are additional to live load values that are factored until buckling occurs. Plate loadings may be given as data, although NL is usually calculated from the total longitudinal load on the panel or
Book•
30 Nov 1991
TL;DR: In this article, the authors present an analysis of the impact of different types of materials on the strength of a single-ply composite and conclude that the effect of different materials on Laminate Strength is dependent on the type of materials and the properties of the composite.
Abstract: 1 Introduction.- 1.1 Fibrous Composites.- 1.2 FRP Constituents.- 1.3 Reinforcement Types.- 1.4 Types of Materials.- 1.5 Terminology.- 2 Ply Stiffness Analysis.- 2.1 Isotropic Ply.- 2.2 Specially Orthotropic Ply.- 2.3 Generally Orthotropic Ply.- 2.4 Transformation of Elastic Constants.- 2.5 Typical Elastic Properties.- 3 Ply Strength Analysis.- 3.1 Isotropic Ply.- 3.2 Orthotropic Ply.- 3.3 Failure Criteria.- 3.4 Sign of Shear Stresses.- 3.5 Choice of Failure Criterion.- 3.6 Typical Strength Properties.- 4 Layered Laminate.- 4.1 Beam Constitutive Equation.- 4.2 Laminate Constitutive Equation.- 4.3 Laminate Notation.- 4.4 Equivalent Elastic Constants.- 5 Laminate Stiffness Analysis.- 5.1 Stiffness Formulation Procedure.- 5.2 Laminate Configuration Types.- 5.3 Symmetric SOPL: Isotropic Plies.- 5.4 Symmetric SOPL: Specially Orthotropic Plies.- 5.5 Symmetric SOPL: Generally Orthotropic Plies.- 5.6 Symmetric MOPL: Isotropic Plies.- 5.7 Symmetric MOPL: Generally Orthotropic Plies.- 5.8 Symmetric MOPL: Cross-ply.- 5.9 Symmetric MOPL: Angle-ply.- 5.10 Symmetric MOPL: Quasi-isotropic.- 5.11 Antisymmetric MOPL: Cross-ply.- 5.12 Antisymmetric MOPL: Angle-ply.- 5.13 Estimated Membrane Elastic Constants.- 5.14 Laminate Stiffness: Summary.- 6 Laminate Strength Analysis.- 6.1 First-Ply-Failure (FPF) Procedure.- 6.2 FPF: Symmetric Laminate-Membrane Load.- 6.3 FPF: Symmetric Laminate-Bending Load.- 6.4 FPF: Unsymmetric Laminate-Membrane Load.- 6.5 Last-Ply-Failure (LPF) Procedure.- 6.6 LPF: Complete Ply Failure-Membrane Load.- 6.7 LPF: Partial Ply Failure-Membrane Load.- 6.8 LPF: Complete Ply Failure-Bending Load.- 6.9 Estimated Laminate Strength.- 6.10 Laminate Strength: Summary.- 7 Residual Stresses.- 7.1 Compound Isotropic Beam.- 7.2 Laminate Thermal Stresses.- 7.3 Determining Thermal Residual Stresses.- 7.4 Constant Temperature Distribution.- 7.5 Hygroscopic Diffusion Mechanism.- 7.6 Laminate Hygroscopic Stresses.- 7.7 Constant and Linear Moisture Distribution.- 7.8 Influence on Laminate Strength.- 7.9 Typical Physical Properties.- 8 Thin-Walled Composite Sections.- 8.1 Assumptions and Axes Systems.- 8.2 Axial Force.- 8.3 Symmetrical Bending.- 8.4 Unsymmetrical Bending.- 8.5 Shear Forces.- 8.6 Torsion of Open Sections.- 8.7 Torsion of Closed Sections.- 9 Interlaminar Stresses.- 9.1 Free Edge Effects.- 9.2 Interlaminar Stress: fxz.- 9.3 Interlaminar Stresses: fyz and fz.- 9.4 Prediction Methods.- 9.5 Effect of Different Stacking Sequences.- 10 Miscellaneous Topics.- 10.1 Holes in Laminates.- 10.2 Buckling of Laminates.- 10.3 Computer Aided Laminate Analysis.- 10.4 FE Method: Line Elements.- 10.5 FE Method: Shell Elements.- 10.6 Test Methods.
TL;DR: In this paper, the free vibration analysis of homogeneous and laminated doubly curved shells on rectangular planform and made of an orthotropic material has been presented using the three-dimensional elasticity equations.
TL;DR: In this paper, the effects of variation in the lamination and geometric parameters of multilayered composite cylinders on the accuracy of the static and vibrational responses predicted by eight modeling approaches, based on two-dimensional shear-deformation shell theories.
TL;DR: For a two-dimensional anisotropic plate, the Green's function satisfying traction-free boundary conditions around an elliptic hole is developed using Stroh's formalism as mentioned in this paper.
TL;DR: In this paper, large amplitude free flexural vibrations of laminated orthotropic plates were studied using C 0 shear flexible QUAD-8 plate element and the nonlinear governing equations were solved using the direct iteration technique.
TL;DR: In this article, a numerical method is proposed for computing reflection and transmission coefficients of plane waves for any incidence plane through an orthotropic, lossy solid layer, which is used to measure the nine coefficients of the complex stiffness matrix by using ultrasonic waves transmitted through a plate-shaped sample immersed in water.
Abstract: This paper presents a method of characterizing orthotropic and viscoelastic behavior of some composite materials. The purpose is to measure the nine coefficients of the complex stiffness matrix, by using ultrasonic waves transmitted through a plate-shaped sample immersed in water. From a study or propagation in principal planes that has been reported in a previous publication [B. Hosten et al., J. Acoust. Soc. Am. 82, 1763–1770 (1987)], this paper emphasizes heterogeneous mode conversion and propagation through a nonprincipal plane, inside the composite. A numerical method is proposed for computing reflection and transmission coefficients of plane waves for any incidence plane through an orthotropic, lossy solid layer. Numerical calculations of reflection and transmission are compared to experimental data: Amplitudes, wave vectors, and damping vectors are given for a unidirectional graphite/epoxy composite.
TL;DR: In this paper, the authors studied the shear buckling load of laminated composite plates and showed that the buckling strength depends on the direction of the applied load, i.e., bending-twisting coupling stiffnesses.
Abstract: The object of the study was to optimize the shear buckling load of laminated composite plates. The laminates lacked coupling between bending and extension (Bij=0) but had otherwise arbitrary selection of the ply angle variation through the thickness. The plates were rectangular and either simply supported or clamped on all edges. For orthotropic plates, it was seen that there is only one parameter necessary for finding the optimal design for different materials and plate aspect ratios. This parameter can be interpreted as the layup angleθ in a (+/−θ) orthotropic laminate. When bendingtwisting coupling is present, the buckling strength depends on the direction of the applied load. A laminate with non-zero bending-twisting coupling stiffnesses can be described with four lamination parameters. The allowable region of these parameters was investigated, and an optimization of the buckling load within this region was performed. It was seen that even this is a one parameter problem. This parameter can be interpreted as the layup anlgeθ in an off-axis unidirectional laminate (θ).
TL;DR: In this article, the dynamic response of an orthotropic elastic half plane subjected to a set of time-harmonic buried loadings is investigated, and the governing differential equations are established in terms of displacements and a general solution is derived using Fourier integral transforms with respect to the xcoordinate.
Abstract: The dynamic response of an orthotropic elastic half plane subjected to a set of time‐harmonic buried loadings is investigated. The governing differential equations are established in terms of displacements and a general solution is derived using Fourier integral transforms with respect to the x‐coordinate. The boundary‐value problems corresponding to time‐harmonic vertical and horizontal loads acting in the interior of the half plane are solved. Explicit analytical solutions are presented for displacements and stresses due to buried uniformly distributed and concentrated loadings. Some characteristics of the analytical solution are investigated, and its numerical evaluation is also discussed. Selected numerical results for displacements and stresses of isotropic, ice, layered soil, and cadmium half‐plane regions are presented. A discussion of these numerical solutions is presented to investigate the influence of the degree of material anisotropy, frequency of excitation, and the type of loading on the res...
TL;DR: In this article, a higher-order shear deformation theory is presented for the analysis of laminated anisotropic shells of revolution, based on realistic approximation of the in-plane displacements through the thickness.
TL;DR: In this article, a continuum mechanics approach is adopted to develop a constitutive model for the nonlinear behaviour of laminated composites up to and including ultimate failure, which is derived within the framework of rate-independent theory of orthotropic plasticity.
Abstract: A continuum mechanics approach is adopted herein to develop a constitutive model for the nonlinear behaviour of laminated composites up to and including ultimate failure. The proposed model for single layers of fibre-reinforced composites (FRC) is derived within the framework of rate-independent theory of orthotropic plasticity. Both unidirectional and bidirectional (e.g., woven) FRC layers are modelled. The individual layer constitutive equations are superimposed using classical lamination theory to yield the global laminate response. The model's accuracy is illustrated by comparing the results of numerical simulations with experimental data available in the literature.
TL;DR: In this paper, the authors presented finite-element formulations for the analysis of reinforced concrete solids based on the modified compression field theory (MCFT), which can be implemented into existing linear elastic algorithms for nonlinear analysis capabilities.
Abstract: Finite‐element formulations are presented for the analysis of reinforced concrete solids. Cracked reinforced concrete is treated as an orthotropic nonlinear elastic material based on a smeared, rotating crack model. Secant‐stiffness moduli are defined for concrete and reinforcement, and these are used in the development of an eight‐noded regular hexahedral element. Procedures are discussed by which the formulations can be implemented into existing linear elastic algorithms to provide nonlinear analysis capabilities. The constitutive relations implemented in the formulations are relations extrapolated from the two‐dimensional models of the modified compression field theory (MCFT). The accuracy of the constitutive models and finite‐element formulations are examined by analyzing a series of overreinforced beams subjected to bending and torsion. Excellent agreement is found between predicted and observed response. The performance characteristics and potential applications of the analysis procedure are discuss...
TL;DR: In this paper, the anisotropy of the filament wound woven structure is modeled as an orthotropic domain employing the concept of angle-ply sublaminates, and the effective orthotropic conductivity tensor incorporates the effect of winding angle.
Abstract: In filament winding of thermoplastics, localized melting/solidification can reduce the residual stresses and allow for improved dimensional stability and performance. This paper presents a three-dimensional thermal analysis for melting and consolidating impregnated tows in the presence of a local heat source during filament winding of thermoplastic composites. The analysis is performed using an Eulerian approach. The anisotropy of the filament wound woven structure is modeled as an orthotropic domain employing the concept of angle-ply sublaminates. The effective orthotropic conductivity tensor incorporates the effect of winding angle. The governing equations are discretized in a nonuniform mesh domain and solved using a finite difference approach. The processing parameters, such as winding angle, winding speed, and heat input, as well as material properties, are incorporated into the analysis. The results show large thermal gradients in the vicinity of the consolidation point. The effects of winding speed and heat input are investigated, and the overall thermal characterization of the process is discussed. The accuracy of the numerical method is assessed by comparing the results of a test problem with an available analytical solution.
08 Apr 1991
TL;DR: In this paper, the in-plane and flexural stiffness of a laminated composite plate are modeled as functions of the lamination parameters that are the functions of their stacking sequences.
Abstract: When laminated composite plates are symmetric and orthotropic, their in-plane and flexural stiffnesses become the functions of the lamination parameters that are the functions of their stacking sequences. We use the lamination parameters as fundamental design variables in designing laminates. The feasible region of the lamination parameters is obtained on a two-dimensional plane. Optimum design points can be obtained from the geometric relations between the feasible region and an objective function
TL;DR: In this article, the problem of finding the optimal orientation of orthotropic properties for an elastic body, subjected to a plane state of stress, in order to maximize the stiffness of the body itself is addressed.
Abstract: The paper deals with the problem of finding the optimal orientation of orthotropic properties for an elastic body, subjected to a plane state of stress, in order to maximize the stiffness of the body itself
TL;DR: In this paper, an arbitrary shaped rigid strip foundation is embedded in an orthotropic elastic soil and the foundation is subjected to time-harmonic vertical, horizontal and moment loadings, and the boundary value problem related to an embedded foundation is analyzed by using the indirect boundary integral equation method.
Abstract: This study is concerned with the dynamic response of an arbitrary shaped rigid strip foundation embedded in an orthotropic elastic soil. The foundation is subjected to time-harmonic vertical, horizontal and moment loadings. The boundary-value problem related to an embedded foundation is analysed by using the indirect boundary integral equation method. The kernel functions of the integral equations are displacement and traction Green's functions of an anisotropic elastic half plane
TL;DR: In this article, a general formulation for the buckling of anisotropic, symmetric, angle-ply composite laminates under linearly varying, uniaxial compressive force using the energy method in conjunction with orthogonal polynomial sequences, generated by a Gram-Schmidt process is presented.
Abstract: In composite structures characterized by lightweight, thin‐walled members, the linear buckling load is one of the most important design considerations. Plate structures (bridge decks and ship hulls) are often subjected to differential compression due to nonuniform bending during their service life. This paper presents a general formulation for the buckling of rectangular, anisotropic, symmetric, angle‐ply composite laminates under linearly varying, uniaxial compressive force using the energy method in conjunction with orthogonal polynomial sequences, generated by a Gram‐Schmidt process. Orthogonal polynomials provide a simpler and efficient tool for handling complex combinations of simple and clamped boundaries. The present study highlights the unusual insensitivity of the buckling load of anisotropic laminates to fiber orientation under in‐plane tension‐compression‐type loading. Such behavior is not known to exist under idealized loading of constant, uniaxial compression, and orthotropic material behavio...
TL;DR: In this paper, the Fouier transfrom technique was applied to the stress analysis of media subjected to applied surface tractions and the solutions were obtained based on the Fourier transformer technique together with the aid of he stiffness matrix approach.
Abstract: The stress analysis of media subjected to applied surface tractions is performed. The solutions are obtained based on the Fouier transfrom technique together with the aid of he stiffness matrix approach. It can be uniformly applied to media with transversely isotropic, orthotropic, and monoclinic layers