Julio C. Massa

A Strength of Materials Formulation for Thin Walled Composite Beams with Torsion

A simple methodology for the analysis of thin walled composite beams subjected to bending, torque, shear, and axial forces is developed. Members with open or closed cross section are considered. The cross section is modeled as a collection of flat. arc-circular, and concentrated area segments. Each laminated segment is modeled with the constitutive equations of classical lamination theory accounting for a linear distribution of normal and shear strains through the thickness of the walls, thus allowing for greater accuracy than classical thin walled theory when the walls are moderately thick. The geometric properties used in classical beam theory such as area, first moment of area, center of gravity, etc., are no longer used because of the variability of the materials properties in the cross section. Instead, mechanical properties such as axial stiffness, mechanical first moment of area. mechanical center of gravity, etc., are defined to incorporate both the geometry and the material properties. Warping, restriction to warping, and secondary stresses are considered. Failure predictions are made with customary failure criteria. Comparison with experimental results are presented.

Modified Unsteady Vortex-Lattice Method to Study Flapping Wings in Hover Flight

A numerical-simulation tool is developed that is well suited for modeling the unsteady nonlinear aerodynamics of flying insects and small birds as well as biologically inspired flapping-wing micro air vehicles. The present numerical model is an extension of the widely used three-dimensional general unsteady vortex-lattice model and provides an attractive compromise between computational cost and fidelity. Moreover, it is ideally suited to be combined with computational structural dynamics to provide aeroelastic analyses. The present numerical results for a twisting, flapping wing with neither leading-edge nor wing-tip separations are in close agreement with the results obtained in previous studies with the Euler equations and a vortex-lattice method. The present results for unsteady lift, mean lift, and frequency content of the force are in good agreement with experimental data for the robofly apparatus. The actual wing motion of a hovering Drosophila is used to compute the flowfield and predict the lift ...

Development of a Kinematical Model to Study the Aerodynamics of Flapping-Wings

The kinematics that characterizes the “natural flight” of insects is quite complex. It involves simultaneous rotations, oscillations and significant changes in the angle of attack. All this permits the wings to follow an extremely complex trajectory producing different flight mechanisms that are efficient at low to moderate Reynolds numbers. Some of these mechanisms, such as the delayed stall, the additional circulation generated by the rotation of the wing, and the wake capture amongst others, offer unique advantages with respect to the well-known fixed-wing aerial vehicles. Such advantages are better lift and thrust generation without the need to increase weight. This paper presents a general kinematical model that permits studying the movements of the wings of a scale robot of a house fly, the ‘RoboFly’, built at UC Berkeley, USA. Additionally, this general kinematical model allows studying the kinematics of the wings of a flying insect considering both the body orientation and the stroke plane orientation of the creature in the 3D space. This work provides a nexus between the descriptive language used by biologists and the predictive language used by engineers. This connection between scientific disciplines allows one to study and characterize the principal kinematic parameters that intervene in a stroke cycle, as well as to determine how these variables modify the trajectories of the material points on the wings.

Computation and Uncertainty Evaluation of Offset Yield Strength

This paper presents computer procedures for the calculation of offset yield strength (Sy) and for the evaluation of the uncertainty in its computation. Offset yield strength is obtained from the plot of stress-strain data recorded in a tension test, as the stress that corresponds to the intersection between the stress-strain curve and a line parallel to its proportional region (offset by a prescribed strain). In the proposed method, the problem is reduced to finding the point of intersection between two straight lines, one that fits the curve in the neighborhood of the intersection and the offset line. For the fitting of each line, we propose the use of a weighted total least-squares algorithm that takes into account uncertainties in both ordinates and abscissas. The evaluation of the uncertainty associated with Sy, in accordance with the Guide to the Expression of Uncertainty in Measurement, considers the correlation between the parameters involved in its calculation. The implementation of these procedures motivated the development of dedicated software for the computation of tensile parameters from tension-test raw data and for the estimation of their associated uncertainties. To validate the program, developed in MATLAB as a standalone application, we used a set of ASCII data curves that have agreed values for the tensile parameters and which are publicly available at the web site of the National Physical Laboratory of the United Kingdom. Using these curves we demonstrate the validity of the proposed method for the computation of Sy; to validate the uncertainty-evaluation procedure, we use the law of propagation of probability distributions through Monte Carlo simulation. The computational tool, whose capabilities are presented in this work, is currently being used at the Laboratory of Mechanical Testing of the National Institute of Industrial Technology (INTI), in Cordoba, Argentina.

Dynamics of Micro-Air-Vehicles with Flapping Wings: A Multibody System Approach

This paper presents the development of a dynamic model to study the flight mechanics of a micro-air-vehicle with flapping wings. This model is based on Lagranges equations for constrained systems. The micro-air-vehicle is modeled as a collection of three rigid bodies a central body and two wings. The wings have prescribed motions relative to the central body, i.e., they are kinematically driven. The numerical integration of all the governing equations, which are differential-algebraic, is performed simultaneously and interactively in the time domain. The integration scheme couples a 4th-order predictor-corrector method, the modified method of Hamming, with a procedure to stabilize the resulting differential-algebraic equations.

Computation of Tensile Strain-Hardening Exponents through the Power-Law Relationship

Many metals flow in the region of uniform plastic deformation following a power-law relationship, which states that true stress is proportional to true-plastic strain raised to the power n. The exponent n, known as the tensile strain-hardening exponent, can be determined from a tension test through appropriate transformations of stress-strain data and least-squares fitting of a straight line. Procedures for the computation of n have been standardized by ASTM International and ISO. Current ASTM and ISO standards differ, most notably, in the type of strain used in calculations. The ASTM procedure permits the use of true strain (true-elastic strain plus true-plastic strain), when true-elastic strain represents less than 10 % of total strain. On the other hand, the ISO version stipulates the subtraction of true-elastic strain from true strain, using a formula whose derivation is not publicly available. In this work, we revisit the expressions that enable the transformation of engineering stress-strain data to true-stress and true-plastic-strain values. Using eight tension-test curves from several materials, obtained through ASCII files publicly available at the website of the National Physical Laboratory of the United Kingdom, we compare n-values obtained via three definitions of strain: (i) true strain, (ii) conventional definition of true-plastic strain, and (iii) true-plastic strain according to the ISO formula. In addition, we investigate the dependency of the results on the strain range over which n-values are calculated. To evaluate strain-range dependency, which arises when metals do not closely follow the power-law relationship, we analyze the effect of strain intervals of increasing length and study the variation of n-values when the range of interest is divided into subintervals. To improve the approximation given by the power-law relationship over the region under analysis, we propose an alternative formulation in which the strength coefficient and the strain-hardening exponent are functions of true-plastic strain.