VIBRATIONS OF PRESTRESSED VARIABLE STIFFNESS COMPOSITE AEROSPACE STRUCTURES BY RITZ APPROACH

With the introduction of the variable stiffness concept, the design space for highperformance lightweight composite structures has expanded significantly. A larger design space, in particular, allows designers to find more effective solutions with higher overall stiffness and fundamental frequency when considering prestressed dynamically excited aerospace components. In this context, an efficient and versatile Ritz method for the transient analysis of prestressed variable stiffness laminated doubly-curved shell structures is presented. The considered theoretical framework is the first-order shear deformation theory without further assumptions on the shallowness or on the thinness of the structure. A rational Bézier surface representation is adopted for the description of the shell allowing general orthogonal surfaces to be represented. General stacking sequences are considered and the unknown displacement field is approximated by Legendre orthogonal polynomials. Stiffened variable angle tow shell structures are modelled as an assembly of shell-like domains and penalty techniques are used to enforce the displacement continuity of the assembled multidomain structure and the kinematical boundary conditions. For the transient analysis of prestressed variable stiffness structures, classical Rayleigh damping is considered and solutions are obtained through the Newmark integration scheme. The proposed approach is validated by comparison with literature and finite elements results and original solutions are presented for prestressed free and forced vibrations of VS stiffened shell structure, proving the ability of the present method in dealing with the analysis of complex aerospace structures.

An Improvement on the Upper Bounds of the Partial Derivatives of NURBS Surfaces

The Non-Uniform Rational B-spline (NURBS) surface not only has the characteristics of the rational Bézier surface, but also has changeable knot vectors and weights, which can express the quadric surface accurately. In this paper, we investigated new bounds of the first- and second-order partial derivatives of NURBS surfaces. A pilot study was performed using inequality theorems and degree reduction of B-spline basis functions. Theoretical analysis provides simple forms of the new bounds. Numerical examples are performed to illustrate that our method has sharper bounds than the existing ones.

Computer Aided Geometric Design of Two-Parameter Freeform Motions

This paper brings together the notion of analytically defined two-parameter motion in Theoretical Kinematics and the notion of freeform surfaces in Computer Aided Geometric Design (CAGD) to develop methods for computer aided design of two-parameter freeform motions. In particular, a rational Bézier representation for two-parameter freeform motions is developed. It has been shown that the trajectory surface of such a motion is a tensor-product rational Bézier surface and that such a kinematically generated surface has a geometric as well as a kinematic control structure. The results have not only theoretical interest in CAGD and kinematics but also applications in CAD/CAM and Robotics.