Conceptual-level evaluation of a variable stiffness skin for a morphing wing leading edge

A morphing leading edge produces a continuous aerodynamic surface that has no gaps between the moving and fixed parts. The continuous seamless shape has the potential to reduce drag, compared to conventional devices, such as slats that produce a discrete aerofoil shape change. However, the morphing leading edge has to achieve the required target shape by deforming from the baseline shape under the aerodynamic loads. In this paper, a conceptual-level method is proposed to evaluate the morphing leading edge structure. The feasibility of the skin design is validated by checking the failure index of the composite when the morphing leading edge undergoes the shape change. The stiffness of the morphing leading edge skin is spatially varied using variable lamina angles, and comparisons to the skin with constant stiffness are made to highlight its potential to reduce the actuation forces. The structural analysis is performed using a two-level structural optimisation scheme. The first level optimisation is applied to find the optimised structural proper- ties of the leading edge skin and the associated actuation forces. The structural properties of the skin are given as a stiffness distribution, which is controlled by a B spline interpolation function. In the second level, the design solution of the skin is investigated. The skin is assumed to be made of variable stiffness composite. The stack sequence of the composite is optimised element-by-element to match the target stiffness. A failure criterion is employed to obtain the failure index when the leading edge is actuated from the baseline shape to the target shape. Test cases are given to demonstrate that the optimisation scheme is able to provide the stiffness distribution of the leading edge skin and the actuation forces can be reduced by using a spatially variable stiffness skin

Assessment criteria for 2D shape transformations in animation

The assessment of 2D shape transformations (or morphing) for animation is a difficult task because it is a multi-dimensional problem. Existing morphing techniques pay most attention to shape information interactive control and mathematical simplicity. This paper shows that it is not enough to use shape information alone, and we should consider other factors such as structure, dynamics, timing, etc. The paper also shows that an overall objective assessment of morphing is impossible because factors such as timing are related to subjective judgement, yet local objective assessment criteria, e.g. based on shape, are available. We propose using “area preservation” as the shape criterion for the 2D case as an acceptable approximation to “volume preservation” in reality, and use it to establish cases in which a number of existing techniques give clearly incorrect results. The possibility of deriving objective assessment criteria for dynamics simulations and timing under certain conditions is discussed

Binary morphological shape-based interpolation applied to 3-D tooth reconstruction

In this paper we propose an interpolation algorithm using a mathematical morphology morphing approach. The aim of this algorithm is to reconstruct the $n$-dimensional object from a group of (n-1)-dimensional sets representing sections of that object. The morphing transformation modifies pairs of consecutive sets such that they approach in shape and size. The interpolated set is achieved when the two consecutive sets are made idempotent by the morphing transformation. We prove the convergence of the morphological morphing. The entire object is modeled by successively interpolating a certain number of intermediary sets between each two consecutive given sets. We apply the interpolation algorithm for 3-D tooth reconstruction

Morphing of Triangular Meshes in Shape Space

We present a novel approach to morph between two isometric poses of the same non-rigid object given as triangular meshes. We model the morphs as linear interpolations in a suitable shape space $\mathcal{S}$. For triangulated 3D polygons, we prove that interpolating linearly in this shape space corresponds to the most isometric morph in $\mathbb{R}^3$. We then extend this shape space to arbitrary triangulations in 3D using a heuristic approach and show the practical use of the approach using experiments. Furthermore, we discuss a modified shape space that is useful for isometric skeleton morphing. All of the newly presented approaches solve the morphing problem without the need to solve a minimization problem.Comment: Improved experimental result

Programming temporal morphing of self-actuated shells

Advances in shape-morphing materials, such as hydrogels, shape-memory polymers and light-responsive polymers have enabled prescribing self-directed deformations of initially flat geometries. However, most proposed solutions evolve towards a target geometry without considering time-dependent actuation paths. To achieve more complex geometries and avoid self-collisions, it is critical to encode a spatial and temporal shape evolution within the initially flat shell. Recent realizations of time-dependent morphing are limited to the actuation of few, discrete hinges and cannot form doubly curved surfaces. Here, we demonstrate a method for encoding temporal shape evolution in architected shells that assume complex shapes and doubly curved geometries. The shells are non-periodic tessellations of pre-stressed contractile unit cells that soften in water at rates prescribed locally by mesostructure geometry. The ensuing midplane contraction is coupled to the formation of encoded curvatures. We propose an inverse design tool based on a data-driven model for unit cells’ temporal responses

Multi-objective optimization for the geometry of trapezoidal corrugated morphing skins

Morphing concepts have great importance for the design of future aircraft as they provide the opportunity for the aircraft to adapt their shape in flight so as to always match the optimal configuration. This enables the aircraft to have a better performance, such as reducing fuel consumption, toxic emissions and noise pollution or increasing the maneuverability of the aircraft. However the requirements of morphing aircraft are conflicting from the structural perspective. For instance the design of a morphing skin is a key issue since it must be stiff to withstand the aerodynamic loads, but flexible to enable the large shape changes. Corrugated sheets have remarkable anisotropic characteristics. As a candidate skin for a morphing wing, they are stiff to withstand the aerodynamic loads and flexible to enable the morphing deformations. This work presents novel insights into the multi-objective optimization of a trapezoidal corrugated core with elastomer coating. The geometric parameters of the coated composite corrugated panels are optimized to minimize the in-plane stiffness and the weight of the skin and to maximize the flexural out-of-plane stiffness of the skin. These objective functions were calculated by use of an equivalent finite element code. The gradient-based aggregate method is selected to solve the optimization problem and is validated by comparing to the GA multi-objective optimization technique. The trend of the optimized objectives and parameters are discussed in detail; for example the optimum corrugation often has the maximum corrugation height. The obtained results provide important insights into the design of morphing corrugated skins

Symmetric Shape Morphing for 3D Face and Head Modelling

We propose a shape template morphing approach suitable for any class of shapes that exhibits approximate reflective symmetry over some plane. The human face and full head are examples. A shape morphing algorithm that constrains all morphs to be symmetric is a form of deformation regulation. This mitigates undesirable effects seen in standard morphing algorithms that are not symmetry-aware, such as tangential sliding. Our method builds on the Coherent Point Drift (CPD) algorithm and is called Symmetry-aware CPD (SA-CPD). Global symmetric deformations are obtained by removal of asymmetric shear from CPD's global affine transformations. Symmetrised local deformations are then used to improve the symmetric template fit. These symmetric deformations are followed by Laplace-Beltrami regularized projection which allows the shape template to fit to any asymmetries in the raw shape data. The pipeline facilitates construction of statistical models that are readily factored into symmetrical and asymmetrical components. Evaluations demonstrate that SA-CPD mitigates tangential sliding problem in CPD and outperforms other competing shape morphing methods, in some cases substantially. 3D morphable models are constructed from over 1200 full head scans, and we evaluate the constructed models in terms of age and gender classification. The best performance, in the context of SVM classification, is achieved using the proposed SA-CPD deformation algorithm