Atila Barut

Analysis of thick sandwich construction by a {3,2}-order theory

Abstract This study is an extension of the {1,2}-order plate theory to a higher order {3,2} theory. Based on the equivalent single-layer assumptions, the in-plane and transverse displacement components are expressed as cubic and quadratic expansions through the thickness of the sandwich construction. Also, the transverse stress component is assumed to vary as a cubic function through the thickness. Utilizing Reissner’s definitions for kinematics of thick plates, the displacement components at any point on the plate are approximated in terms of weighted-average quantities (displacements and rotations) that are functions of the in-plane coordinates. The undetermined coefficients defining the in-plane and transverse displacement fields are then expressed in terms of the weighted-average displacements and rotations and their derivatives by directly employing Reissner’s definitions and enforcing the zero transverse-shear-stress conditions on the upper and lower surfaces of the sandwich panel. The coefficients defining the transverse stress component are obtained by requiring the transverse strain component, which is expressed in terms of the unknown coefficients of the transverse stress component from a mixed constitutive relation, to be the least-squares equivalent of the kinematic definition of the transverse strain component. The resulting expressions for the unknown coefficients of the transverse stress component are related to resultant strains and curvatures defined from kinematic relations. The equations of equilibrium and boundary conditions of the sandwich plate based on the {3,2}-higher-order theory are derived by employing the principles of virtual displacements. The robustness and accuracy of this {3,2}-order plate theory are established through comparisons with exact solutions available in the literature. The finite element implementation of the present {3,2}-order plate theory is also discussed.

Bolted double-lap composite joints under mechanical and thermal loading

This study concerns the determination of the contact stresses and contact region around bolt holes and the bolt load distribution in single- and double-lap joints of composite laminates with arbitrarily located bolts under general mechanical loading conditions and uniform temperature change. The unknown contact stress distribution and contact region between the bolt and laminates and the interaction among the bolts require the bolt load distribution, as well as the contact stresses, to be as part of the solution. The present method is based on the complex potential theory and the variational formulation in order to account for bolt stiffness, bolt-hole clearance, and finite geometry of the composite laminates.

Analysis of singular stress fields at junctions of multiple dissimilar materials under mechanical and thermal loading

Abstract Traditional finite element analyses of the stress state in regions with dissimilar materials are incapable of correctly resolving the stress state because of the unbounded nature of the stresses. A finite element technique utilizing a coupled global (special) element with traditional elements is presented. The global element includes the singular behavior at the junction of dissimilar materials with or without traction-free surfaces. A hybrid global (special) element is developed utilizing the exact solution for the stress and displacement fields based on the eigenfunction expansion method under mechanical and thermal loading. The global element for arbitrary geometrical and material configurations, not limited to a few dissimilar material sectors, is interfaced with traditional local (conventional) elements while satisfying the inter-element continuity. The coupling between the hybrid global element and conventional finite elements is implemented into ansys , a commercially available finite element program. Also, the global element is integrated into the ansys graphical user interface for pre- and post-processing.

Buckling of a thin, tension-loaded, composite plate with an inclined crack

Abstract A numerical study of the local buckling and fracture response of a thin composite plate with an inclined crack and subjected to tension is presented. Local buckling of the unsupported edges of the crack occurs due to compressive stresses caused by a Poisson effect in the neighborhood of the crack. The relationship between fracture of a plate with a crack and the local buckling and postbuckling responses of the plate is established through a geometrically nonlinear finite-element analysis in conjunction with concepts from fracture mechanics. The analysis is based on a co-rotational form of the updated Lagrangian formulation that is implemented with a triangular shell element that includes transverse shear deformation effects. The potential energy release rate results are computed for a predetermined radial crack propagation direction that coincides with the location of the maximum stationary strain energy density near the crack tip. The results indicate that the local buckling load increases and the potential energy release rate decreases as the crack orientation changes from a transverse crack to a longitudinal crack aligned with the direction of the applied tension load. The effect of stacking sequence on the local buckling load and on the energy release rate for specific crack orientations is also discussed.

Nonlinear analysis of laminates through a mindlin-type shear deformable shallow shell element

Abstract This study presents a nonlinear analysis with application to a doubly curved shallow shell element free of ‘locking’. The ‘locking’ phenomenon is eliminated by explicitly determining the shear and membrane correction factors. The element formulation utilizes the Reissner-Mindlin and Marguerre theories. The analysis of thin and moderately thick composite shells undergoing large displacements and rotations is achieved by using the corotational form of an updated Lagrangian formulation. The validity of the analysis is established by correlating present results with various benchmark cases that involve large displacements and rotations, as well as elastic stability.

Nonlinear deformations of flapping wings on a micro air vehicle

Wing kinematics and wing flexibility are critical to MAV designs because they affect the wing planform, as well as the shape of the airfoil, such as camber and thickness. Therefore, the effect of structural deformations on the aerodynamic performance of a MAV is significant. Such analysis is rather complex due to the many inherent complexities in the flow arising from a wide variety of flow conditions and the presence of moving and deforming boundaries arising from the flapping flexible/deformable wings. The wings are highly flexible and can undergo large deformations as a result of the aerodynamic loading. This deformation can, in turn, have a significant effect on the flow, which can then alter the loading itself. In this study, the presence of aerodynamic loads is not included in order to simplify the analysis so that only the effect of prescribed dynamic motion and wing flexibility on the wing deformations can be investigated. Unlike previous studies, the present study includes the effect of externally applied dynamic loads and time-dependent angular velocity and the influence of the coupling among the rigid-body motion, large elastic deformations, and inertial forces on the motion and deformation of the wing. In particular, this study simulates the motion of a dragonfly, which is representative of MAVs.

A shear-flexible facet shell element for large deflection and instability analysis

Abstract A facet shell element based on an anisoparametric plate bending element and a quadratic plane-stress element with vertex rotations is formulated for geometrically nonlinear analysis of shells. The updated Lagrangian formulation which proves to be effective for three-node elements is employed. The restriction of small rotation between the increments is removed by using Hsiaos finite rotation method in which the rigid body motion is eliminated from the total displacement. The displacement control is used to alleviate the singularity of the tangential stiffness matrix in the limit point type problems. Numerical solutions are presented for beams, plates and shells to evaluate the performance of the element.

Analysis method for bonded patch repair of a skin with a cutout

This study presents an analysis method for determining the transverse shear and normal stresses in the adhesive and in-plane stresses in the repair patch and in the repaired skin. The damage to the skin is represented in the form of a cutout. The circular or elliptical cutout can be located arbitrarily under the patch. The patch is free of external tractions while the skin is subjected to general loading along its external edge. The method utilizes the principle of minimum potential energy in conjunction with complex potential functions to analyze a patch-repaired damage configuration. The present results have been validated against experimental measurements and three-dimensional finite element (FE) predictions concerning the patch repair of a circular cutout in a skin under uniform loading.

Equivalent single-layer theory for a complete stress field in sandwich panels under arbitrarily distributed loading

Abstract In single-layer theory, the displacement components represent the weighted-average through the thickness of the sandwich panel. Although discrete-layer theories are more representative of sandwich construction than the single-layer theories, they suffer from an excessive number of field variables in proportion to the number of layers. In this study, utilizing Reissner’s definitions for kinematics of thick plates, the displacement components at any point on the plate are approximated in terms of weighted-average quantities (displacements and rotations) that are functions of the in-plane coordinates. The equations of equilibrium and boundary conditions of the sandwich panel are derived by employing the principle of virtual displacements. The solution for an arbitrarily distributed load is obtained by employing Fourier series representations of the unknown field variables. This single-layer theory is validated against an analytical solution for simply supported square sandwich panels under pressure over a small region on the face sheet and is also compared with previous single-layer plate theories.

A new stiffened shell element for geometrically nonlinear analysis of composite laminates

Abstract A new stiffened shell element combining shallow beam and shallow shell elements is developed for geometrically nonlinear analysis of stiffened composite laminates under mechanical loading. The formulation of this element is based on the principle of virtual displacements in conjunction with the co-rotational form of the total Lagrangian description of motion. In the finite element formulation, both the shell and the beam (stiffener) elements account for transverse shear deformations and material anisotropy. The cross section of the stiffener (beam) can be arbitrary in geometry and lamination. In order to combine the stiffener with the shell element, constraint conditions are applied to the displacement and rotation fields of the stiffener. These constraint conditions ensure that the cross section of the stiffener remains co-planar with the shell section after deformation. The resulting expressions for the displacement and rotation fields of the stiffener involve only the nodal unknowns of the shell element, thus reducing the total number of degrees-of-freedom. Also, the discretization of the entire stiffened shell structure becomes more flexible. The robustness of the stiffened shell element has been proven by comparison against other shell elements considered previously.