Isogeometric iFEM analysis of thin shell structures

Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated

A comparison of smooth basis constructions for isogeometric analysis

In order to perform isogeometric analysis with increased smoothness on complex domains, trimming, variational coupling or unstructured spline methods can be used. The latter two classes of methods require a multi-patch segmentation of the domain, and provide continuous bases along patch interfaces. In the context of shell modeling, variational methods are widely used, whereas the application of unstructured spline methods on shell problems is rather scarce. In this paper, we therefore provide a qualitative and a quantitative comparison of a selection of unstructured spline constructions, in particular the D-Patch, Almost-$C^1$, Analysis-Suitable $G^1$ and the Approximate $C^1$ constructions. Using this comparison, we aim to provide insight into the selection of methods for practical problems, as well as directions for future research. In the qualitative comparison, the properties of each method are evaluated and compared. In the quantitative comparison, a selection of numerical examples is used to highlight different advantages and disadvantages of each method. In the latter, comparison with weak coupling methods such as Nitsche's method or penalty methods is made as well. In brief, it is concluded that the Approximate $C^1$ and Analysis-Suitable $G^1$ converge optimally in the analysis of a bi-harmonic problem, without the need of special refinement procedures. Furthermore, these methods provide accurate stress fields. On the other hand, the Almost-$C^1$ and D-Patch provide relatively easy construction on complex geometries. The Almost-$C^1$ method does not have limitations on the valence of boundary vertices, unlike the D-Patch, but is only applicable to biquadratic local bases. Following from these conclusions, future research directions are proposed, for example towards making the Approximate $C^1$ and Analysis-Suitable $G^1$ applicable to more complex geometries

Geometry and tool motion planning for curvature adapted CNC machining

CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing. We demonstrate this at hand of 5-axis machining of freeform surfaces, where the degrees of freedom in selecting and moving the cutting tool allow one to adapt the tool motion optimally to the surface to be produced. We aim at a high-quality surface finish, thereby reducing the need for hard-to-control post-machining processes such as grinding and polishing. Our work is based on a careful geometric analysis of curvature-adapted machining via so-called second order line contact between tool and target surface. On the geometric side, this leads to a new continuous transition between “dual” classical results in surface theory concerning osculating circles of surface curves and oscu- lating cones of tangentially circumscribed developable surfaces. Practically, it serves as an effective basis for tool motion planning. Unlike previous approaches to curvature-adapted machining, we solve locally optimal tool positioning and motion planning within a single optimization framework and achieve curvature adaptation even for convex surfaces. This is possible with a toroidal cutter that contains a negatively curved cutting area. The effectiveness of our approach is verified at hand of digital models, simulations and machined parts, including a comparison to results generated with commercial software

Active feed array compensation for reflector antenna surface distortions

The feasibility of electromagnetic compensation for reflector antenna surface distortions is investigated. The performance characteristics of large satellite communication reflector antenna systems degrade as the reflector surface distorts, mainly due to thermal effects from solar radiation. The technique developed can be used to maintain the antenna boresight directivity and sidelobe level independent of thermal effects on the reflector surface. With the advent of monolithic microwave integrated circuits (MMIC), a greater flexibility in array fed reflector antenna systems can be achieved. MMIC arrays provide independent control of amplitude and phase for each of the many radiating elements in the feed array. By assuming a known surface distortion profile, a simulation study is carried out to examine the antenna performance as a function of feed array size and number of elements. Results indicate that the compensation technique can effectively control boresight directivity and sidelobe level under peak surface distortion in the order of tenth of a wavelength

Some Extensions Of Log Aesthetic Curves And Its Acceleration Using General Processing Unit (GPU)

The first part investigates the characteristics of Log Aesthetic Curve (LAC). The second part proposes new techniques to accelerate the computation of line of curvature (LoC) by using General Processing Unit (GPU) and the last part is to implement the LACs to the surface equations

The continuous wavelet transform on conic sections

We review the known construction of the continuous wavelet transform (CWT) on the two-sphere. Next we describe the construction of a CWT on the upper sheet of a two- sheeted hyperboloid, emphasizing the similarities between the two cases. Finally we give some indications on the CWT on a paraboloid and we introduce a unified approach to the CWT on conic sections

Properties of interstellar wind leading to shape morphology of the dust surrounding HD 61005

A structure formed by dust particles ejected from the debris ring around HD 61005 is observed in the scattered light. The main aim here is to constrain interstellar wind parameters that lead to shape morphology in the vicinity of HD 61005 using currently available observational data for the debris ring. Equation of motion of 2 $\times$ 10$^5$ dust particles ejected from the debris ring under the action of the electromagnetic radiation, stellar wind, and interstellar wind is solved. A two-dimensional (2D) grid is placed in a given direction for accumulation of the light scattered on the dust particles in order to determine the shape morphology. The interaction of the interstellar wind and the stellar wind is considered. Groups of unknown properties of the interstellar wind that create the observed morphology are determined. A relation between number densities of gas components in the interstellar wind and its relative velocity is found. Variations of the shape morphology caused by the interaction with the interstellar clouds of various temperatures are studied. When the interstellar wind velocity is tilted from debris ring axis a simple relation between the properties of the interstellar wind and an angle between the line of sight and the interstellar wind velocity exists. Dust particles that are most significantly influenced by stellar radiation move on the boundary of observed structure. Observed structure at HD 61005 can be explained as a result of dust particles moving under the action of the interstellar wind. Required number densities or velocities of the interstellar wind are much higher than that of the interstellar wind entering the Solar system.Comment: 11 pages, 7 figures, accepted to A&