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Marek-jerzy Pindera - One of the best experts on this subject based on the ideXlab platform.
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Parametric finite-volume method for Saint Venant’s torsion of arbitrarily shaped cross sections
Composite Structures, 2021Co-Authors: Heze Chen, Jose Gomez, Marek-jerzy PinderaAbstract:Abstract We extend our recent finite-volume based approach to the solution of Saint Venant’s torsion problems of bars and beams comprised of rectangular sections to enable analysis of arbitrary cross sections characterized by curved boundaries. This is accomplished by incorporating parametric mapping based on transfinite grid generation to enable discretization of the bar cross section by quadrilateral rather than rectangular subvolumes employed in the original version. The construction of the Local Stiffness Matrix that relates the surface-averaged subvolume warping functions to the corresponding tractions is carried out in the reference plane such that the subvolume equilibrium in the physical plane is satisfied in a surface-averaged sense. This produces explicit expressions for the Stiffness Matrix elements that may be readily coded. Orthotropic subvolumes are intrinsic in the method’s construction so that bars with heterogeneous and composite microstructures may be analyzed. The convergence and accuracy of the parametric finite-volume method are assessed and verified upon comparison with exact elasticity solutions for cross sections with convex and concave boundaries. Examples involving structural applications of prismatic bars with curved boundaries illustrate the utility of the developed methodology. These include cross sections that resemble biological constructs with homogeneous and graded regions aimed at enhancing torsional rigidities, as well as homogeneous and graded elliptical cross sections with orthotropic shear moduli aimed at reducing and eliminating warping. We demonstrate for the first time that by laminating an elliptical cross section with alternating stiff and soft isotropic layers in a manner that mimics the required orthotropic moduli at the homogenized level, warping can be practically eliminated with sufficient microstructural refinement.
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Generalized FVDAM theory for elastic–plastic periodic materials
International Journal of Plasticity, 2016Co-Authors: Márcio Cavalcante, Marek-jerzy PinderaAbstract:Abstract Generalized FVDAM theory for the analysis of periodic heterogeneous materials with elastic–plastic phases undergoing infinitesimal deformation is constructed to overcome the limitations of the original or 0th-order version of the theory, and to concomitantly extend the theory's range of modeling capabilities. The 0th-order theory suffers from intrinsic constraints stemming from limited displacement field representation at the Local level, which results in the deterioration of pointwise continuity of interfacial tractions and displacements with increasing plasticity, requiring greater unit cell discretization. The generalization is based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain, in contrast with the second-order expansion employed in the 0th-order theory. The higher-order displacement field is expressed in terms of elasticity-motivated surface-averaged kinematic variables which are subsequently related to corresponding static variables through a generalized Local Stiffness Matrix. Comparison of Local fields in metal Matrix composites with large moduli contrasts obtained using the generalized FVDAM theory, its predecessor and finite-element method illustrates substantial improvement in the pointwise satisfaction of interfacial continuity conditions at adjacent subvolume faces in the presence of plasticity, producing smoother stress and plastic strain distributions and excellent interfacial conformability with smaller unit cell discretizations. The generalized theory offers several advantages relative to the Q9-based finite-element method, including direct relationship between static and kinematic variables across subvolume faces and superior satisfaction of pointwise traction continuity which facilitate modeling of various interfacial phenomena, such as fiber/Matrix cracks illustrated herein.
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Generalized Finite-Volume Theory for Elastic Stress Analysis in Solid Mechanics—Part I: Framework
Journal of Applied Mechanics, 2012Co-Authors: Márcio Cavalcante, Marek-jerzy PinderaAbstract:A generalized finite-volume theory is proposed for two-dimensional elasticity problems on rectangular domains. The generalization is based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain, in contrast with the second-order expansion employed in our standard theory. The higher-order displacement field is expressed in terms of elasticity-based surface-averaged kinematic variables, which are subsequently related to corresponding static variables through a Local Stiffness Matrix derived in closed form. The novel manner of defining the surface-averaged kinematic and static variables is a key feature of the generalized finite-volume theory, which provides opportunities for further exploration. Satisfaction of subvolume equilibrium equations in an integral sense, a defining feature of finite-volume theories, provides the required additional equations for the Local Stiffness Matrix construction. The theory is constructed in a manner which enables systematic specialization through reductions to lower-order versions. Part I presents the theoretical framework. Comparison of predictions by the generalized theory with its predecessor, analytical and finite-element results in Part Il illustrates substantial improvement in the satisfaction of interfacial continuity conditions at adjacent subvolume faces, producing smoother stress distributions and good interfacial conformability.
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Generalized Finite-Volume Theory for Elastic Stress Analysis in Solid Mechanics—Part II: Results
Journal of Applied Mechanics, 2012Co-Authors: Marcio A. A. Cavalcante, Marek-jerzy PinderaAbstract:In Part I, a generalized finite-volume theory was constructed for two-dimensional elasticity problems on rectangular domains based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain. The higher-order displacement field was expressed in terms of elasticity-based surface-averaged kinematic variables that were subsequently related to corresponding static variables through a Local Stiffness Matrix derived in closed form. The theory was constructed in a manner that enables systematic specialization through reductions to lower-order versions, including the original theory based on a quadratic displacement field representation, herein called the zeroth-order theory. Comparison of predictions generated by the generalized theory with its predecessor, analytical and finite-element results in Part II illustrates substantial improvement in the satisfaction of interfacial continuity conditions at adjacent subvolume faces, producing smoother stress distributions and good interfacial conformability. While in certain instances the first-order theory produces acceptably smooth stress distributions, concentrated loadings require the second-order (generalized) theory to reproduce stress and displacement fields with fidelity comparable to analytical and finite-element results.
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Finite-volume direct averaging micromechanics of heterogeneous materials with elastic–plastic phases☆
International Journal of Plasticity, 2006Co-Authors: Yogesh Bansal, Marek-jerzy PinderaAbstract:Abstract In this communication, we extend the recently re-constructed micromechanics model called high-fidelity generalized method of cells (Bansal, Y., Pindera, M.-J., 2005. A second look at the higher-order theory for periodic multiphase materials. J. Appl. Mech. 72 (2), 177–195.) by incorporating inelastic response capability for the individual phases. The re-construction, based on the Local/global Stiffness Matrix approach, has simplified the model’s theoretical framework and substantially increased its computational efficiency as well as implementability, enabling analysis of unit cells with realistic multiphase microstructures previously unattainable in the original formulation developed by Aboudi et al. (Aboudi, J., Pindera, M-J., Arnold, S.M., 2001. Linear thermoelastic higher-order theory for periodic multiphase materials. J. Appl. Mech. 68 (5), 697–707; Aboudi, J., Pindera, M-J, Arnold, S.M., 2003. Higher-order theory for periodic multiphase materials with inelastic phases. Int. J. Plasticity 19 (6), 805–847.) with an accuracy approaching finite-element solutions. Just as importantly, the re-construction has revealed the model to be based on a finite-volume, direct averaging approach with clearly discernible similarities to, and differences with, the finite-element method and the finite-volume technique used in computational fluid mechanics. Herein, easily programmable closed-form expressions have been derived for the thermo-inelastic contributions to the Local Stiffness Matrix equations that facilitate incorporation of different inelastic constitutive theories for the phase response. The re-constructed model is then employed to investigate orientational and architectural effects in unidirectional metal Matrix composites characterized by multi-inclusion unit cells. Classical incremental plasticity theory with isotropic hardening is employed for the Matrix response for consistency and comparison with previously reported results by Aboudi et al. (2003). Unit cells representative of a square array of fibers rotated by an angle about the fiber axis, which lack planes of material symmetry in the rotated coordinate system in which the micromechanical analysis is performed, belong in the first category. New results are presented for such rotated unidirectional porous composites which suggest guidelines for optimizing Stiffness and ductility of this class of light-weight materials relative to dominant loading directions. Strengthening effects due to fiber clustering, which require highly discretized multi-inclusion unit cells, fall in the second category. It is demonstrated that the previously documented results for particulate composites, explained by the clustering-induced alteration of stress invariants which govern plastic strain evolution, are recovered for unidirectional composites as well.
Márcio Cavalcante - One of the best experts on this subject based on the ideXlab platform.
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Generalized FVDAM theory for elastic–plastic periodic materials
International Journal of Plasticity, 2016Co-Authors: Márcio Cavalcante, Marek-jerzy PinderaAbstract:Abstract Generalized FVDAM theory for the analysis of periodic heterogeneous materials with elastic–plastic phases undergoing infinitesimal deformation is constructed to overcome the limitations of the original or 0th-order version of the theory, and to concomitantly extend the theory's range of modeling capabilities. The 0th-order theory suffers from intrinsic constraints stemming from limited displacement field representation at the Local level, which results in the deterioration of pointwise continuity of interfacial tractions and displacements with increasing plasticity, requiring greater unit cell discretization. The generalization is based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain, in contrast with the second-order expansion employed in the 0th-order theory. The higher-order displacement field is expressed in terms of elasticity-motivated surface-averaged kinematic variables which are subsequently related to corresponding static variables through a generalized Local Stiffness Matrix. Comparison of Local fields in metal Matrix composites with large moduli contrasts obtained using the generalized FVDAM theory, its predecessor and finite-element method illustrates substantial improvement in the pointwise satisfaction of interfacial continuity conditions at adjacent subvolume faces in the presence of plasticity, producing smoother stress and plastic strain distributions and excellent interfacial conformability with smaller unit cell discretizations. The generalized theory offers several advantages relative to the Q9-based finite-element method, including direct relationship between static and kinematic variables across subvolume faces and superior satisfaction of pointwise traction continuity which facilitate modeling of various interfacial phenomena, such as fiber/Matrix cracks illustrated herein.
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Homogenization of periodic materials with viscoelastic phases using the generalized FVDAM theory
Computational Materials Science, 2014Co-Authors: Márcio Cavalcante, Severino P. C. MarquesAbstract:In the last decades, new generations of advanced materials have been designed and manufactured for specific applications. The micromechanics plays an important role in the development of heterogeneous materials, enabling efficient analyses of composite materials with complex geometries, circumventing the traditional trial-and-error approach, producing substantial cost savings. The unit cell problem to the analysis of periodic heterogeneous media can be solved by the well-established 0th order version of the finite-volume theory, named finite-volume direct averaging micromechanics (FVDAM) theory. This standard version of the FVDAM theory employs an incomplete second-order displacement field within individual subvolumes of a discretized analysis domain together with a surface-averaging framework, which does not enforce displacement or traction continuity in a point-wise manner. This, in turn, produces interfacial interpenetrations and non-traction stress discontinuities, thereby demanding very refined meshes in order to produce good interfacial conformability and pointwise stress continuity between adjacent subvolumes. To overcome these shortcomings, a generalized FVDAM theory has been proposed to enable analysis of periodic heterogeneous materials in the finite-deformation domain. The generalization is based on a higher-order displacement field representation and on the definition of elasticity-based surface-averaged kinematic and static variables related through a Local Stiffness Matrix. Herein, we specialize the generalized FVDAM theory to the infinitesimal analysis of periodic materials with viscoelastic phases, where a total or secant formulation is employed, with the viscoelastic strains evaluated incrementally using an algorithm based on the concept of state variables. The generalized or 2nd order version considerably improves interfacial conformability and pointwise traction and non-traction stress continuity between adjacent subvolumes in comparison with the 0th order version, but with a higher computational cost. Furthermore, for the same mesh discretization, these two versions provide comparable macroscopic response. Considering these features, the 0th order version is recommended to evaluate the effective elastic properties and the homogenized creep and relaxation functions, while the 2nd order version is more efficient in the evaluation of the microscopic displacement and stress fields.
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Generalized Finite-Volume Theory for Elastic Stress Analysis in Solid Mechanics—Part I: Framework
Journal of Applied Mechanics, 2012Co-Authors: Márcio Cavalcante, Marek-jerzy PinderaAbstract:A generalized finite-volume theory is proposed for two-dimensional elasticity problems on rectangular domains. The generalization is based on a higher-order displacement field representation within individual subvolumes of a discretized analysis domain, in contrast with the second-order expansion employed in our standard theory. The higher-order displacement field is expressed in terms of elasticity-based surface-averaged kinematic variables, which are subsequently related to corresponding static variables through a Local Stiffness Matrix derived in closed form. The novel manner of defining the surface-averaged kinematic and static variables is a key feature of the generalized finite-volume theory, which provides opportunities for further exploration. Satisfaction of subvolume equilibrium equations in an integral sense, a defining feature of finite-volume theories, provides the required additional equations for the Local Stiffness Matrix construction. The theory is constructed in a manner which enables systematic specialization through reductions to lower-order versions. Part I presents the theoretical framework. Comparison of predictions by the generalized theory with its predecessor, analytical and finite-element results in Part Il illustrates substantial improvement in the satisfaction of interfacial continuity conditions at adjacent subvolume faces, producing smoother stress distributions and good interfacial conformability.
Donatella L Marini - One of the best experts on this subject based on the ideXlab platform.
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virtual element methods for plate bending problems
Computer Methods in Applied Mechanics and Engineering, 2013Co-Authors: Franco Brezzi, Donatella L MariniAbstract:Abstract We discuss the application of Virtual Elements to linear plate bending problems, in the Kirchhoff–Love formulation. As we shall see, in the Virtual Element environment the treatment of the C 1 -continuity condition is much easier than for traditional Finite Elements. The main difference consists in the fact that traditional Finite Elements, for every element K and for every given set of degrees of freedom, require the use of a space of polynomials (or piecewise polynomials for composite elements) for which the given set of degrees of freedom is unisolvent. For Virtual Elements instead we only need unisolvence for a space of smooth functions that contains a subset made of polynomials (whose degree determines the accuracy). As we shall see the non-polynomial part of our Local spaces does not need to be known in detail, and therefore the construction of the Local Stiffness Matrix is simple, and can be done for much more general geometries.
Guillermo Ramirez - One of the best experts on this subject based on the ideXlab platform.
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FRICTIONLESS CONTACT IN A LAYERED PIEZOELECTRIC MEDIUM COMPOSED OF MATERIALS WITH HEXAGONAL SYMMETRY
2013Co-Authors: Guillermo RamirezAbstract:A Matrix formulation is presented for the solution of frictionless contact problems on arbitrarily multilayeredpiezoelectric half-planes. Different arrangements of elastic and transversely orthotropic piezoelectric materials within themultilayered medium are considered. A generalized plane deformation is used to obtain the governing equilibrium equations for each individual layer. These equations are solved using the infinite Fourier transform technique. The problem isthen reformulated using the Local/global Stiffness method, in which a Local Stiffness Matrix relating the stresses and electricdisplacement to the mechanical displacements and electric potential in the transformed domain is formulated for each layer. Then it is assembled into a global Stiffness Matrix for the entire half-plane by enforcing interfacial continuity of tractions and displacements. This Local/global Stiffness approach not only eliminates the necessity of explicitly finding the unknown Fourier coefficients, but also allows the use of efficient numerical algorithms, many of which have been developed for finite element analysis. Unlike finite element methods, the present approach requires minimal input. Application of the mixedboundary conditions reduces the problem to an integral equation. This integral equation is numerically solved for theunknown contact pressure using a technique based on the Chebyshev polynomials. Resumen: Se presenta una formulacion matricial para la solucion de problemas de contacto sin friccion en semiplanos piezoelectricos elasticos de multiples capas. Se consideran diferentes disposiciones de materiales piezoelectricos elasticos y transversalmente ortotropicos dentro del medio de multiples capas. Se usa una deformacion de plano generalizada para obtener las ecuaciones gobernantes de equilibrio para cada capa individual, que se resuelven con la tecnica de transformada de Fourier infinita. Entonces el problema se reformula con el metodo de rigidez Local/global, en el cual se formula para cada capa una matriz de rigidez Local que relaciona los esfuerzos y el desplazamiento electrico con los desplazamientos mecanicos y el potencial electrico en el dominio transformado. En seguida se ensambla en una matriz de rigidez global para todo el semiplano imponiendo la continuidad interfacial de tracciones y desplazamientos. Este enfoque por rigidez Local/global no solo elimina la necesidad de hallar explicitamente los coeficientes de Fourier desconocidos, sino que tambien permite el uso de algoritmos numericos eficientes, muchos de los cuales se desarrollaron para analisis por elementos finitos. A diferencia de los metodos de elementos finitos, este enfoque requiere una entrada minima. El uso de condiciones de borde mezcladas reduce el problema a una ecuacion integral, que se resuelve para la presion de contacto desconocida con una tecnica basada en los polinomios de Chebyshev.
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Frictionless contact in a layered piezoelectric medium characterized by complex eigenvalues
Smart Materials and Structures, 2006Co-Authors: Guillermo RamirezAbstract:A Local/global Stiffness Matrix formulation is presented to study the response of an arbitrarily multilayered piezoelectric half-plane indented by a rigid frictionless parabolic punch. The methodology is extended to accommodate the presence of piezoelectric layers that are characterized by complex eigenvalues. Different arrangements of elastic and transversely orthotropic piezoelectric materials within the multilayered medium are considered. A generalized plane deformation is used to obtain the governing equilibrium equations for each individual layer. These equations are solved using the infinite Fourier transform technique. The problem is then reformulated using the Local/global Stiffness method, in which a Local Stiffness Matrix relating the stresses and electric displacement to the mechanical displacements and electric potential in the transformed domain is formulated for each layer. Then it is assembled into a global Stiffness Matrix for the entire half-plane by enforcing continuity conditions along the interface. Application of the mixed boundary conditions reduces the problem to an integral equation for the unknown pressure in the contact area. This integral has a divergent kernel that is decomposed into a Cauchy-type and regular parts using the asymptotic properties of the Local Stiffness Matrix. The resulting equation is numerically solved for the unknown contact pressure using a technique based on the Chebyshev polynomials.
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Frictionless contact in a layered piezoelectric half-space
Smart Materials and Structures, 2003Co-Authors: Guillermo Ramirez, Paul R. HeyligerAbstract:A Matrix formulation is presented for the solution of frictionless contact problems on arbitrarily multilayered piezoelectric half-planes. Different arrangements of elastic and piezoelectric materials with hexagonal symmetry within the layered medium are considered. A generalized plane deformation is used to obtain the governing equilibrium equations for each individual layer. These equations are solved using the infinite-Fourier-transform technique. The problem is then reformulated using the Local/global Stiffness method, in which a Local Stiffness Matrix relating the stresses and electric displacements to the mechanical displacements and electrical potentials in the transformed domain is formulated for each layer. Then it is assembled into a global Stiffness Matrix for the entire half-plane by enforcing interfacial continuity of traction forces and displacements. This Local/global approach not only eliminates the necessity of explicitly finding the unknown Fourier coefficients, but also allows the use of efficient numerical algorithms, many of which have been developed for finite-element analysis. Unlike finite-element methods, the Local/global Stiffness approach requires minimal input. Application of the mixed boundary conditions reduces the problem to a singular integral equation. This integral equation is then numerically solved for the unknown contact pressure using a collocation technique. Knowledge of the contact pressure and electrostatic distributions is very important for applications where piezoelectric layers are used as sensors and/or actuators. One example includes the active deformation and shape control of support surfaces.
Pottavathri, Sai Hargav - One of the best experts on this subject based on the ideXlab platform.
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Effect of in-plane fiber tow waviness in the strength characteristics of different fiber reinforced composites
Wichita State University, 2015Co-Authors: Pottavathri, Sai HargavAbstract:Thesis (M.S.)--Wichita State University, College of Engineering, Dept. of Mechanical EngineeringThe purpose of this study was to investigate the strength and effectiveness of certain composite materials when induced by 'in-plane fiber tow waviness' in a composite ply. Fiber waviness is usually induced by infusion processes and inherent in fabric architectures. Composite structural details like ply drops and ply joints can cause serious fiber misalignment. These are usually dependent on parameters such as ply thickness, percentage of plies dropped, and location of ply drop, the gap between the plies, mold geometry and pressure, and pressure of the resin which slides the dry fibers during the resin transfer molding process. Fiber disorientation due to fiber tow waviness in „in-plane‟ direction has been the subject of recent studies on wind turbine blade materials and other aerospace laminates with reports of compression strengths and failure strains that are borderline, depending upon the reinforcement architecture, Matrix resin and environment. Waviness is expected to reduce compressive strength due to two primary factors. The fibers may be oriented in such a way that the geometry that results because of the orientation may exacerbate the basic fiber, strand, or layer buckling mode of failure. The waviness could also shift the fiber orientation of the axis of the ply longitudinal direction which eventually results in Matrix dominated failures for plies normally orientated in the primary load direction (00). The longitudinal tension and compression behavior of unidirectional carbon fiber composite laminates of different materials (different grades of carbon, glass and Kevlar with different resins) were investigated using finite element analysis tool ABAQUS. Both global and Local stress & strain values generated by the finite element model were validated by the traditional mechanical methods using ply/Local Stiffness Matrix and global/reduced Stiffness Matrix. A precise geometry of waviness on different materials was modeled with different wave severity factor and a parametric study was conducted. Three different defects were modeled where the angle of misalignment ranged from 5 to 15 degrees with a wavelength ranged from 1 inch to 1.5 inches and amplitude which ranged from 0.05 inches to 0.1 inches. This revealed the effect of 'in-plane fiber tow waviness' on the stress distribution and loss of strength in carbon-reinforced composite materials. The results clearly show that the effect of 'in-plane fiber tow waviness' leads to resin rich areas which causes high stress concentrations and decrease in the strength ratio, leading to delamination's
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Effect of in-plane fiber tow waviness in the strength characteristics of different fiber reinforced composites
Wichita State University. Graduate School, 2015Co-Authors: Pottavathri, Sai HargavAbstract:Presented to the 11th Annual Symposium on Graduate Research and Scholarly Projects (GRASP) held at the Heskett Center, Wichita State University, April 24, 2015.Research completed at Department of Mechanical Engineering, College of EngineeringThe purpose of this study was to investigate the strength and effectiveness of certain composite materials when induced with 'in-plane fiber tow waviness' in a composite ply. Fiber waviness is usually induced by infusion processes and inherent in fabric architectures. Composite structural details like ply drops and ply joints can cause serious fiber misalignment. These are usually dependent on parameters such as ply thickness, percentage of plies dropped, and location of ply drop, the gap between the plies, mold geometry and pressure, and pressure of the resin which slides the dry fibers during resin transfer molding process. Fiber disorientation due to fiber tow waviness in 'in-plane' direction has been the subject of recent studies on wind turbine blade materials and other aerospace laminates with reports of compression strengths and failure strains that are borderline, depending upon the reinforcement architecture, Matrix resin and environment. Waviness is expected to reduce compressive strength due to two primary factors. The fibers may be oriented in such a way that the geometry that results because of the orientation may exacerbate the basic fiber, strand, or layer buckling mode of failure. The waviness could also shift the fiber orientation off the axis of the ply longitudinal direction which eventually results in Matrix dominated failures for plies normally orientated in the primary load direction (00). The longitudinal tension and compression behavior of unidirectional carbon fiber composite laminates of different materials (different grades of carbon, glass and Kevlar with different resins) were investigated using finite element analysis tool ABAQUS. Both global and Local stress and strain values generated by the finite element model were validated by the traditional mechanics methods using ply/Local Stiffness Matrix and global/reduced Stiffness Matrix. A precise geometry of waviness on different materials was modeled with different wave severity factor and a parametric study was conducted. Three different defects were modeled where the angle of misalignment ranged from 5 to 15 degrees with a wavelength ranged from 1 inch to 1.5 inch and amplitude which ranged from 0.03 inch to 0.1 inch. This revealed the effect of 'in-plane fiber tow waviness' on the stress distribution and loss of strength in carbonreinforced composite materials. The results clearly show that the effect of 'in-plane fiber tow waviness' leads to resin rich areas which causes high stress concentrations and decrease in the strength ratio, leading to delaminations, and damage of the composite panels that are unacceptable for applications that require prolonged environmental exposure and stress cycles.Graduate School, Academic Affairs, University Librarie
