General Lay-up Research Articles

Analysis of thick multilayered anisotropic plates by a higher order plate element

The purpose of the present note is twofold: to give a brief review of a recent generalization of the zig-zag approach to anisotropic multilayered plates of general lay-ups, and to further substantiate the accuracy of the developed eight-noded, curvilinear quadrilateral plate element

Constitutive Relations of a Damaged Composite Laminate with Nonsymmetric Constrained Cracking

The constitutive relations are developed for a damaged composite laminate in which a transversely cracked lamina is nonsymmetrically constrained by neighboring layers. The derivation is based on an approximate elasticity theory approach. The stiffnesses variation in cracked laminates is expressed as a function of the crack density. The stiffness degradation for the cracked laminates with more general layups can be predicted by using these relations.

A finite strip analysis of cracked laminates

As a step towards the construction of a comprehensive model for damaged composites, the deformation of transversely cracked laminates is analysed. The approach is based on a generalised plane strain approach and uses the finite strip method which allows general lay-ups of laminates rather than just cross-ply to be considered. General loading is treated. In addition, the method permits a more flexible control to be exercised between accuracy and the extensiveness of the calculations than can be achieved using existing analyses. This method could be integrated with the finite element analysis of structures to allow for changes in the effective material properties of locally damaged regions. Results produced by the approach are compared with those available in the literature and good agreement is demonstrated.

Stress Determination at Skin-Stiffener Interfaces of Composite Stiffened Panels Under Generalized Loading

An approach is presented to calculate stresses at the skin-stiffener inter faces of composite stiffened panels. The skin and stiffener can have general anisotropic layup and the loading can be in-plane or out-of-plane as long as the in-plane stresses far from the flange edge can be at most linear in the out-of-plane direction. A stress-based en ergy minimization is used with a variational calculus derivation of the governing equa tions. All six stresses are determined at the skin-stiffener interface. Comparison of the present closed form solution with a finite element solution shows good agreement. The stresses determined with the present method are used in a failure criterion to predict onset of delamination. The effects of geometry and layup on the onset of delamination for various loadings are investigated and several trend curves useful for design applications are presented.

Desmear — The Key Processes for Reliable Through‐plating of Printed Circuitry

The paper describes in detail the basics of manufacturing printed circuits and all relevant interactions with the currently used methods of desmearing. A matrix proposes the optimal method to choose depending on the given needs of an application. The first part discusses the general layup of printed circuits, the commonly used sequences of manufacturing, different types of construction and, of most importance to the desmear processes, the polymeric nature of widely used laminates. Single processes of the through‐plating sequence, as well as the consequences of desmearing for subsequent assembly operations, are highlighted. An overview of currently used methods of desmearing is given with respect to commonly used process parameters as well as the basics of the relevant chemical reactions. The second part of the paper focuses on selection of the optimal desmear method, depending on the nature of the material for a given application, namely the different polymers utilised in rigid, rigid‐flex and microwave circuits. The paper ends with a survey of practical ways to monitor the process capability of any desmear process.

Buckling and vibration of thin laminated composite, prismatic shell structures

A description is given of the multi-term, finite strip analysis of the free vibration and buckling, under a system of applied biaxial direct and shear stresses, of thin, prismatic shell structures. The walls of the structure may be composite laminates with a general lay-up. The analysis is based on the use of Koiter-Sanders thin shell theory. Combinations of diaphragm, clamped and free conditions at the two ends of a structure are incorporated. The displacement field of a transversely-curved finite strip utilises Bernoulli-Euler beam functions in the longitudinal direction and quintic polynomial representations in the circumferential direction. The superstrip concept is used in conjunction with the modified Sturm sequence-bisection approach to provide an efficient analysis capability. Several applications involving flat plates, curved plates and complete cylinders are detailed.

Some observations on the modeling of laminated composite beams with general lay-ups

In this paper the modeling of laminated beams has been considered by a systematic reduction of the constitutive relations of the three-dimensional anisotropic body. The basic equations of the beam theory here are those of the parabolic shear deformation theory. Numerical results for natural frequencies and the Euler buckling load have been presented using the present modeling of the constitutive relations and those of the conventional type modeling. It has been observed from the numerical results that the two approaches differ little in the case of cross-ply laminates but there exists a considerable difference (by a multiple factor of 3 in some cases) in the case of angle-ply laminates. The correctness of the present modeling has been further verified by modeling the same beam as a plate. It has been concluded that one should adopt the constitutive relations as given in this paper while modeling the laminated, especially angle-ply, composite beams.

Thermal expansion coefficients for laminates obtained from invariant lamina properties

The coefficients of thermal expansion for laminates made from unidirectional, fibre-reinforced lamina are presented in terms of thermal expansion invariants of the orthotropic lamina, and certain lamination integrals. The results are arranged in tabular form which facilitates the optimisation procedures necessary to achieve the desired coefficients of thermal expansion for given design criteria. Coordinate transformations for the linear coefficients of thermal expansion of individual lamina are presented in terms of multiple angle relationships from which invariants for the expansion coefficients are identified. It is shown however, that, unlike laminate stiffness properties, the linear coefficients of thermal expansion for a laminate having a general lay-up sequencing do not conform to such invariant relationships. An equivalent isotropic coefficient of thermal expansion parameter for composite material is developed; it is suggested that this can be viewed as an intrinsic material property which can be used as a design tool for comparing the overall thermal strain response of composites to that of other materials. Characteristic values for this equivalent expansion parameter for several fibre-reinforced composite materials are presented.