Journal of Aerospace Engineering

During the 1970s, Wachspress developed shape functions for convex n-gons as polynomials of $n-2$ degree divided by the one of $n-3\text{.}$ Originated from projective geometry these interpolants are linear on the sides and can exactly reproduce arbitrary linear fields. Here an alternative derivation is presented. The wide availability of computer algebra programs makes these high accuracy elements accessible. Associated C++ codes are particularly suited for large scale finite element analysis employed in the aerospace industry.

Engineering mechanics formulations of aerospace industry problems overwhelmingly rely upon spatial averaging techniques. Crucial applications in the area of dynamic response analysis and stochastic estimation of material degradation can be cited as important cases. Integration procedures on finite domains underlie physically acceptable averaging processes. Unlike one-dimensional cases, integrals within arbitrary areas and volumes cannot be approximated by a Gaussian form of numerical quadrature. Here the divergence theorem is applied once and twice, respectively, for polygonal and polyhedral integration domains, to construct integrals on boundary wireframes. The sum of Gaussian quadrature values on linear segments of the wireframe yields the final result of numerical integration on a finite element.

This paper is concerned with designing an optimum composite flexible wing structure to enhance flutter speed by imposing modal frequency distribution constraints and comparing it with an optimum design obtained with the flutter velocity constraint. The composite wing is subjected to three flight conditions to satisfy stress constraints in addition to modal frequency distribution or flutter constraints. The multidisciplinary optimization system ASTROS was used for this study. This study indicates that flutter velocity of a wing structure can be enhanced with less increase in the weight of the structure by using frequency distribution constraints than flutter velocity constraint. In the case of a design with modal frequency constraints, the distribution of the ±45° and 90° fiber layers provided required stiffness distribution in order to produce an acceptable solution with less increase in weight than the design obtained with flutter velocity constraint. It is speculated that the required stiffness change in order to achieve necessary modal frequency separation can be achieved to prevent flutter by providing a system of “smart” actuating elements distributed within the internal substructure of a wing.

This paper describes the validation of a Lagrange-Rayleigh-Ritz technique for the mathematical modeling of mass loaded panels for active control studies. The validation has been carried out by comparing the results produced by a Lagrange-Rayleigh-Ritz model with the results produced by a finite-element model and experimental data. Attention was focussed on a simply supported panel with a lumped mass constrained to its surface to simulate the presence of equipment mounted on the panel and twin piezoelectric patches bonded to the panel, working as sensors and actuators. The design of the experimental rig is described in detail, and a test campaign was carried out to obtain a set of transfer functions characteristic of this plant. The experimental data are then used to validate the predictions of the mathematical model. In particular, it was demonstrated that the Lagrange-Rayleigh-Ritz model was able to reproduce accurately the dynamics of the plant requiring a relatively small number of degrees of freedom.

A small satellite is likely to tumble as the result of separating from the rocket. It is therefore very important to capture it promptly with finite magnetic torque. Magnetic torque is orthogonal to the external magnetic field; therefore, it is impossible to generate precisely the control torque that would be required according to simple control theories. However, it is possible to define the desirable torque first and then derive from this the actual control torque. A criteria is presented for this derivation and two control algorithms are formulated, based on nonlinear design theories. One is the energy method that takes the Lyapunov function as a control criteria and uses a divided districts control algorithm to determine the desirable torque. The other one uses the variable structure control method to define the desirable torque. The results of computer simulation indicated that these algorithms have the advantages of excellent robustness and are easily designed and realized.