Manabendra Das

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.

Coupled BEM and FEM Analysis of Functionally Graded Material Layers

ABSTRACT This study presents the development of a boundary element method (BEM) capable of including functionally graded materials in order to capture the correct behavior of the underfill material in electronic packages. In order to take advantage of the salient features of both FEM and BEM, this study also couples the BEM solution with the conventional FEM solution while satisfying the continuity of displacements and equilibrium of tractions along the interfaces.

Digital Image Correlation for Adhesive Strains in Bonded Composite Lap Joints

The use of digital image correlation (DIC) is explored as a viable method for measuring the displacements within the adhesive regions of double-lap joints. Building upon previous experience involving the use of non-contact displacement measurements in thermal and simple mechanical loading situations, the DIC technique is further explored and extended to measure displacements in double-lap joints. Measured displacements in double-lap joints are then compared to the numerical predictions from a special-purpose in-house finite elementbased bonded joint analysis method. The resulting comparison serves to validate both the use of DIC as a suitable method for measurements within the adhesive and the numerical predictions of the displacement fields in the adhesives within lap joints.

Nonlinear Flexible Multibody Dynamic Analysis of Rotor Blades with a Trailing Edge Flap

This study presents a novel nonlinear multibody approach for the structural modeling of helicopter blades. Unlike the conventional approach of using beam elements to represent the rotor blade, the present analysis utilizes a plate element, which assumes a nonlinear strain measure and rotation, as well as transverse shear deformation. The principle of virtual work is used to derive the equations of motion. Kinematic joints are modeled by a set of constraint equations, which are invoked in the formulation through the coordinate partitioning method. The capability of the present analysis is demonstrated by considering the structural dynamics response of a composite helicopter blade with a trailing edge flap. Composite materials are being extensively used in rotorcrafts, and an accurate analysis must include the effect of motion-induced stiffness in both the longitudinal (span-wise) and chord-wise directions and the coupling of the nonlinear elastic deformation with the overall dynamic motion. Most of the multibody dynamic analyses of rotor blades are limited to beam-type approximations. In a commonly accepted approach, the three-dimensional and geometrical nonlinear elasticity problem is reduced to two problems. 2 One is a geometrically nonlinear one- dimensional problem of a beam in the span-wise direction and the other is a two-dimensional linear elasticity problem from which the beams cross-sectional properties at a span-wise station are determined. As required by this type of reduction, a number of blade models have emerged with various levels of refinement. These models have the advantage of being simple, and there is a significant reduction in the number of degrees of freedom as compared to a three-dimensional model without any reduction. However, the complete three-dimensional models do not involve any assumptions related to the modeling of the cross section, and no complicated post-processing technique is required to recover the complete displacement field. In order to achieve an optimum balance between accuracy and computational efficiency, this study utilizes a plate element for a complete three-dimensional analysis of the rotor blade. The model is able to capture all the necessary characteristics associated with composite rotor blades, such as transverse shear deformation, cross-section warping, and elastic coupling caused by material anisotropy and geometric nonlinearities. One of the major focus areas of the helicopter industry is to reduce the vibratory load at the source, before it propagates to the fuselage. Recently, the actively controlled trailing edge flap (ACF) has attracted much attention for

Folded Plate Structures Undergoing Large Membrane and Transverse Bending Deformations

A shell element that is well suited for the analysis of folded plate and shell structures is presented. In contrast to unfolded plates, the walls of folded plates can undergo substantial amount of transverse as well as membrane bending. For instance, in a rotor blade, the flange and web of a spar undergo transverse and membrane bending under flap bending, respectively, and the reverse occurs under lag bending. Therefore, a suitable shell-element technology should accurately model the transverse-bending and membrane-bending deformations, while maintaining kinematic compatibility along the element edges. The new shell element incorporates the Assumed Natural DEviatoric Strain (ANDES) and anisoparametric element formulations. The element robustness is established by comparisons with experimental measurements and other numerical predictions.

Three-dimensional analysis of sandwich panels with common defects

This study presents the application of a new triangular finite element for modeling thick sandwich panels based on a {3,2}-order single-layer plate theory. This new computationally efficient element captures the correct variation of deformations and stresses in the thickness direction, as they are evaluated from a posteriori calculations of equilibrium equations. The capability of this element is demonstrated by considering a sandwich panel with two common defect configurations under various loading conditions. The defects are introduced as a circular cutout in facesheet and a cylindrical cavity in the core. Introduction As illustrated in Fig. 1, defects in sandwich panels may arise from hail strikes, tool drop, bird impact, and runway debris hits. Due to the manufacturing process and mechanical properties of the facesheets and the core materials, the most common modes of impact damage are indentation of facesheet and core crushing. These types of defects are commonly observed in sandwich panels serving as part of control surfaces, and pose a major maintenance and repair concern for the airlines. Therefore, an accurate and robust strength analysis of the damaged sandwich panels is essential to predict the influence of the damage, which is necessary for establishing allowable damage limits. This requires an accurate assessment of the stress and displacement fields. Stress analysis of sandwich panels with defects is a formidable task because of the presence of dissimilar materials and sharp changes in geometry. In addition, computational difficulties arise because the thickness of the constituent layers is highly disproportionate to the in-plane dimensions. Analysis of sandwich panels with common defects can be performed by employing standard threedimensional finite elements or elements based on the layer-wise (zig-zag) theory. Although these elements _______________ *Graduate Research Assistant, Department of Aerospace and Mechanical Engineering, Student Member AIAA. Assistant Research Professor, Department of Aerospace and Mechanical Engineering. ‡Professor, Department of Aerospace and Mechanical Engineering, Member AIAA. Copyright

Coupled BEM and FEM analysis of functionally graded underfill layers in electronic packages

This study presents the development of a robust general purpose boundary element method (BEM) capable of including functionally graded materials (FGM) in order to capture the correct behavior of the underfill material accurately. BEM requires discretization only along the boundary while satisfying the governing equations exactly within the domain. The BEM is inherently more accurate than the FEM as it treats both displacements and tractions as primary variables while displacements are the only primary variables in the FEM. In order to take advantage of the salient features of both FEM and BEM, this study also couples the BEM solution with the conventional FEM solution while satisfying the continuity of displacements and equilibrium of tractions along the interfaces. The FEM-BEM coupling is demonstrated by using the super-element capability of ANSYS/spl reg/, a commercially available finite element program.

A Refined and Efficient Approach for Dynamic Analysis of Helicopter Blades

This study presents an application of a three-dimensional approach for detailed analysis of an articulated rotor blade undergoing large displacement and elastic deformations. The articulated blade has the geometry, structural and mass properties similar to the UH60 blade. In analyzing an articulated blade, each member of the cross-section is modeled individually. The titanium box-beam and the Graphite-Epoxy skin are modeled using plate elements, the homogeneous core is modeled using solid elements. Lumped mass is used to represent the balance weight. One dimensional spring and damper are also utilized to model the pitch link and the lead–lag damper. A quasi-steady aerodynamic model based on the lifting line theory has been utilized to compute the aerodynamic load. A wind tunnel trim analysis has been utilized to compute the control setting that are required to produce a specific thrust and eliminate the 1/rev flapping motion.

A Geometrically Nonlinear Shell Element Based on Higher- Order Theory for Sandwich Panels

A higher-order flat triangular shell element is formulated for geometrically nonlinear analysis of sandwich panels. The element utilizes the kinematic assumptions of a recently developed {3,2}-order plate theory, where the in-plane displacements are expanded cubically and the transverse displacement has a parabolic distribution through the thickness. The kinematics accommodates the in-plane, transverse shear, and transverse normal modes of deformation. The linear plate element based on the {3,2}-order kinematics has previously been established and the element’s predictive capability successfully validated. In this effort, the linear element is extended to account for the nonlinear strains arising from large deflections. To obtain the nonlinear strain fields that are compatible with the linear strain components, the nonlinear part of the Green strain tensor is rewritten in terms of the weighted-average strain resultants that yield the {3,2}-order expansions. The incremental equilibrium equations are obtained via the virtual work principle utilizing the co-rotational updated Lagrangian formalism. The numerical results show that the present nonlinear finite element formulation is capable of accurately predicting the nonlinear response of a wide range of commonly used sandwich panels. I. Introduction ANDWICH construction provides substantial improvement in structural performance while ensuring high bending stiffness at low weight-to-strength ratios. Common to all sandwich construction is a single core with relatively stiff face sheets, or multiple cores with multiple face sheets. The core material, commonly of relatively low density and stiffness, provides continuous support between the face sheets, thus increasing the overall stiffness. Because of the large differences in stiffness properties between the face sheets and the core, their deformation characteristics can be substantially different. The face sheets carry bending moments through the in-plane tensile and compressive stresses. The core material experiences transverse shear and compressive deformations. Transverse shear deformations arise from bending, especially when the core is thick and has a relatively low stiffness. Face sheets undergoing unequal displacements can cause the core to experience transverse compression. Transverse compression may also arise due to a locally distributed load on the face sheets or higher-frequency excitation. In order to enhance the performance of sandwich construction in an optimal way, it is essential to determine the stress fields in the face sheets, in the core, and along their interfaces. However, the assessment of the complete stress and strain fields for sandwich construction, especially in the presence of anisotropic and unequal face sheets, is rather complex. Although sandwich construction can be analyzed using standard three-dimensional finite elements to model the face sheets and the core, such modeling is often computationally too expensive. This is especially the case when the problem includes nonlinearities arising from large deflections, thus requiring iterative methods to be carried out. Alternatively, suitable higher-order shell finite elements that account adequately for the effects of both

Repair Classification for Sandwich Panels with Hail Damage

Hail strikes of possibly exceeding an energy level of 50 Joules may cause multiple-site damage to thin gauged composite airplane structures. If not repaired properly, they may trigger an extensive damage to airplane structures and disruptions to airline operations, and therefore posing a major maintenance and repair concern for the airlines. It is important both for the OEM and the airlines to be able to classify the hail strike damage for appropriate repair procedure. Therefore, this study presents a methodology to assist engineers in the classification of the repair type for hail strike damage. The methodology involves an accurate prediction of the stress and strain fields, and residual strength prediction.