Design of anisotropic plates for improved damage tolerance

An analytical study is presented showing the effects of the notch tip geometry on the location and direction of crack growth from an existing notch in a unidirectional fibrous composite modeled as a homogeneous, anisotropic, elastic material. Anisotropic elasticity and the normal stress ratio theory are used to study crack growth from elliptical notches in unidirectional composites. Sharp cracks, circular holes, and ellipses are studied under far-field tension and shear loading. The capabilities of a previously developed design code was upgraded to handle more generalized plate geometries and laminates under a more generalized loading and boundary conditions. Discussion of the developments of the design code is presented

A compressive failure model for anisotropic plates with a cutout under compressive and shear loads

Failure models for the prediction of compressive strength of plates with a hole are investigated. One of the models is based on the strength failure of the fibers that leads to fiber kinking failure. A different version is developed for cases where shear failure of the fibers is expected to be a dominate failure mode. Both models are capable of including the effects of combined shearing and compressive stresses around a hole in a plate and, therefore, are expected to be applicable to plates under combined shearing and compressive loadings, as well as anisotropic plates

Analysis and Design of Variable Stiffness Composite Cylinders

An investigation of the possible performance improvements of thin circular cylindrical shells through the use of the variable stiffness concept is presented. The variable stiffness concept implies that the stiffness parameters change spatially throughout the structure. This situation is achieved mainly through the use of curvilinear fibers within a fiber-reinforced composite laminate, though the possibility of thickness variations and discrete stiffening elements is also allowed. These three mechanisms are incorporated into the constitutive laws for thin shells through the use of Classical Lamination Theory. The existence of stiffness variation within the structure warrants a formulation of the static equilibrium equations from the most basic principles. The governing equations include sufficient detail to correctly model several types of nonlinearity, including the formation of a nonlinear shell boundary layer as well as the Brazier effect due to nonlinear bending of long cylinders. Stress analysis and initial buckling estimates are formulated for a general variable stiffness cylinder. Results and comparisons for several simplifications of these highly complex governing equations are presented so that the ensuing numerical solutions are considered reliable and efficient enough for in-depth optimization studies. Four distinct cases of loading and stiffness variation are chosen to investigate possible areas of improvement that the variable stiffness concept may offer over traditional constant stiffness and/or stiffened structures. The initial investigation deals with the simplest solution for cylindrical shells in which all quantities are constant around the circumference of the cylinder. This axisymmetric case includes a stiffness variation exclusively in the axial direction, and the only pertinent loading scenarios include constant loads of axial compression, pressure, and torsion. The results for these cases indicate that little improvement over traditional laminates exists through the use of curvilinear fibers, mainly due to the presence of a weak link area within the stiffness variation that limits the ultimate load that the structure can withstand. Rigorous optimization studies reveal that even though slight increases in the critical loads can be produced for designs with an arbitrary variation of the fiber orientation angle, the improvements are not significant when compared to traditional design techniques that utilize ring stiffeners and frames. The second problem that is studied involves arbitrary loading of a cylinder with a stiffness variation that changes only in the circumferential direction. The end effects of the cylinder are ignored, so that the problem takes the form of an analysis of a cross-section for a short cylinder segment. Various load cases including axial compression, pressure, torsion, bending, and transverse shear forces are investigated. It is found that the most significant improvements in load-carrying capability exist for cases which involve loads that also vary around the circumference of the shell, namely bending and shear forces. The stiffness variation of the optimal designs contribute to the increased performance in two ways: lowering the stresses in the critical areas through redistribution of the stresses; and providing a relatively stiff region that alters the buckling behavior of the structure. These results lead to an in-depth optimization study involving weight optimization of a fuselage structure subjected to typical design constraints. Comparisons of the curvilinear fiber format to traditional stiffened structures constructed of isotropic and composite materials are included. It is found that standard variable stiffness designs are quite comparable in terms of weight and load-carrying capability yet offer the added advantage of tailorability of distinct regions of the structure that experience drastically different loading conditions. The last two problems presented in this work involve the nonlinear phenomenon of long tubes under bending. Though this scenario is not as applicable to fuselage structures as the previous problems, the mechanisms that produce the nonlinear effect are ideally suited to be controlled by the variable stiffness concept. This is due to the fact that the dominating influence for long cylinders under bending is the ovalization of the cross-section, which is governed mainly by the stiffness parameters of the cylindrical shell. Possible improvement of the critical buckling moments for these structures is investigated using either a circumferential or axial stiffness variation. For the circumferential case involving infinite length cylinders, it is found that slight improvements can be observed by designing structures that resist the cross-sectional deformation yet do not detract from the buckling resistance at the critical location. The results also indicate that buckling behavior is extremely dependent on cylinder length. This effect is most easily seen in the solution of finite length cylinders under bending that contain an axial stiffness variation. For these structures, the only mechanism that exhibits improved response are those that effectively shorten the length of the cylinder, thus reducing the cross-sectional deformation due to the forced restraint at the ends. It was found that the use of curvilinear fibers was not able to achieve this effect in sufficient degree to resist the deformation, but that ring stiffeners produced the desired response admirably. Thus, it is shown that the variable stiffness concept is most effective at improving the bending response of long cylinders through the use of a circumferential stiffness variation

Optimum design of geodesically stiffened composite plates

With the goal of tailorability in mind, the in-plane stiffness characteristics of a particular grid stiffened plate configuration under axial and shear loads have been studied. The contribution of the skin to the stiffener network and the resultant skin/rib interaction is analyzed. For the given plate geometry and loads, it is shown that an optimum configuration does exist. To achieve optimally designed practical plate configurations, buckling constraints need to be included in the design. Due to the complex geometry and loading of the plates, a simplified local buckling analysis of isolated stiffeners and triangular skin elements between the stiffeners is considered. Development of a stiffener buckling analysis represent stiffeners as shear deformable plate elements is presented

Composite materials for rail transit systems

The potential is explored for using composite materials in urban mass transit systems. The emphasis was to identify specific advantages of composite materials in order to determine their actual and potential usage for carbody and guideway structure applications. The literature was reviewed, contacts were made with major domestic system operators, designers, and builders, and an analysis was made of potential composite application to railcar construction. Composites were found to be in use throughout the transit industry, usually in secondary or auxiliary applications such as car interior and nonstructural exterior panels. More recently, considerable activity has been initiated in the area of using composites in the load bearing elements of civil engineering structures such as highway bridges. It is believed that new and improved manufacturing refinements in pultrusion and filament winding will permit the production of beam sections which can be used in guideway structures. The inherent corrosion resistance and low maintenance characteristics of composites should result in lowered maintenance costs over a prolonged life of the structure

Damage states in laminated composite three-point bend specimens: An experimental-analytical correlation study

Damage states in laminated composites were studied by considering the model problem of a laminated beam subjected to three-point bending. A combination of experimental and theoretical research techniques was used to correlate the experimental results with the analytical stress distributions. The analytical solution procedure was based on the stress formulation approach of the mathematical theory of elasticity. The solution procedure is capable of calculating the ply-level stresses and beam displacements for any laminated beam of finite length using the generalized plane deformation or plane stress state assumption. Prior to conducting the experimental phase, the results from preliminary analyses were examined. Significant effects in the ply-level stress distributions were seen depending on the fiber orientation, aspect ratio, and whether or not a grouped or interspersed stacking sequence was used. The experimental investigation was conducted to determine the different damage modes in laminated three-point bend specimens. The test matrix consisted of three-point bend specimens of 0 deg unidirectional, cross-ply, and quasi-isotropic stacking sequences. The dependence of the damage initiation loads and ultimate failure loads were studied, and their relation to damage susceptibility and damage tolerance of the mean configuration was discussed. Damage modes were identified by visual inspection of the damaged specimens using an optical microscope. The four fundamental damage mechanisms identified were delaminations, matrix cracking, fiber breakage, and crushing. The correlation study between the experimental results and the analytical results were performed for the midspan deflection, indentation, damage modes, and damage susceptibility

Tow-Steered Panels With Holes Subjected to Compression or Shear Loads

Tailoring composite laminates to vary the fiber orientations within a fiber layer of a laminate to address non-uniform stress states and provide structural advantages such as the alteration of principal load paths has potential application to future low-cost, light-weight structures for commercial transport aircraft. Evaluation of this approach requires the determination of the effectiveness of stiffness tailoring through the use of curvilinear fiber paths in flat panels including the reduction of stress concentrations around the holes and the increase in load carrying capability. Panels were designed through the use of an optimization code using a genetic algorithm and fabricated using a tow-steering approach. Manufacturing limitations, such as the radius of curvature of tows the machine could support, avoidance of wrinkling of fibers and minimization of gaps between fibers were considered in the design process. Variable stiffness tow-steered panels constructed with curvilinear fiber paths were fabricated so that the design methodology could be verified through experimentation. Finite element analysis where each element s stacking sequence was accurately defined is used to verify the behavior predicted based on the design code. Experiments on variable stiffness flat panels with central circular holes were conducted with the panels loaded in axial compression or shear. Tape and tow-steered panels are used to demonstrate the buckling, post-buckling and failure behavior of elastically tailored panels. The experimental results presented establish the buckling performance improvements attainable by elastic tailoring of composite laminates

Thermal Testing of Tow-Placed, Variable Stiffness Panels

Commercial systems for precise placement of pre-preg composite tows are enabling technology that allows fabrication of advanced composite structures in which the tows may be precisely laid down along curvilinear paths within a given ply. For laminates with curvilinear tow paths, the fiber orientation angle varies continuously throughout the laminate, and is not required to be straight and parallel in each ply as in conventional composite laminates. Hence, the stiffness properties vary as a function of location in the laminate, and the associated composite structure is called a "variable stiffness" composite structure

Design and Manufacture of Elastically Tailored Tow Placed Plates

Elastic stiffness tailoring of laminated composite panels by allowing the fibers to curve within the plane of the laminate is a relatively novel design concept that has been demonstrated to be both beneficial and practical. In particular, for structures with highly non-uniform stress states, such as the case of a flat panel with a central hole subjected to in-plane loading, the concept is likely to provide substantial improvements in load carrying capability. The objective of the present study is to determine the effectiveness of stiffness tailoring through the use of curvilinear fibers to reduce stress concentrations around the hole and improve the load carrying capability of panels with holes. In this study software was created that translates standard finite element models with traditional laminate definitions into ones that possess stacking sequences with curvilinear fiber paths that are directly manufacturable using an advanced tow placement machine. Preliminary designs for the manufacturing and testing phase were determined through rudimentary design studies for flat plates without holes under axial compression. These candidate designs were then analyzed using finite element models that accurately reflect the test conditions and geometries in order to select final designs for testing. A total of six large panels, measuring three feet by six feet, each of which are used to produce four specimens with or without holes, were fabricated and delivered to NASA for machining and testing

Optimization of Elastically Tailored Tow-Placed Plates with Holes

Elastic stiffness tailoring of laminated composite panels by allowing the fibers to curve within the plane of the laminate is a design concept that has been demonstrated to be both beneficial and practical. The objective of the present paper is to demonstrate the effectiveness of stiffness tailoring through the use of curvilinear fibers to reduce stress concentrations around the hole and improve the load carrying capability of panels. Preliminary panel designs that are to be manufactured and tested were determined through design studies for flat plates without holes under axial compression using an optimization program. These candidate designs were then analyzed with finite element models that accurately reflect the test conditions and geometries in order to decide upon the final designs for manufacture and testing. An advanced tow-placement machine is used to manufacture the test panels with varying fiber orientation angles. A total of six large panels measuring three feet by six feet, each of which is used to produce four specimens with or without holes, are fabricated. The panels were machined into specimens with holes and tested at NASA Langley Research Center. Buckling response and failure of panels without holes and with two different hole dimensions are presented. Buckling and failure loads of tow-steered specimens are significantly greater than the buckling and failure loads of traditional straight-fiber specimens