Bernard Maurin

The surface stress density method as a form-finding tool for tensile membranes

Form-finding for membrane tension structures is a delicate operation which must ensure both the absence of compressive areas and interactive control of the forms generated. Until now, methods have generally been based on large displacements and strain analysis that provide non-linear formulations; resolution and computation are, therefore, too complex and cumbersome. This paper describes a new method of form-finding which reflects a wish to provide architects with a simple, effective and reliable investigation suited to their needs. The surface stress density method uses surface triangular elements with an isotropic stress tensor and leads to an iterative procedure which converges on configurations that satisfy the laws of static equilibrium. Mathematical considerations ensure the convergence conditions. This method enables the designer to generate a broad range of structures (pneumatic membranes or cable-reinforced membranes), while conserving control of shape and internal stress distribution. Moreover, the formulation draws a parallel with the force density method and a combined approach may be specified, particularly for the monitoring of reinforcing cable.

Mechanical model of cytoskeleton structuration during cell adhesion and spreading

The biomechanical behavior of an adherent cell is intimately dependent on its cytoskeleton structure. Several models have been proposed to study this structure taking into account its existing internal forces. However, the structural and geometrical complexities of the cytoskeletons filamentous networks lead to difficulties for determining a biologically realistic architecture. The objective of this paper is to present a mechanical model, combined with a numerical method, devoted to the form-finding of the cytoskeleton structure (shape and internal forces) when a cell adheres on a substrate. The cell is modeled as a granular medium, using rigid spheres (grains) corresponding to intracellular cross-linking proteins and distant mechanical interactions to reproduce the cytoskeleton filament internal forces. At the initial state (i.e., before adhesion), these interactions are tacit. The adhesion phenomenon is then simulated by considering microtubules growing from the centrosome towards transmembrane integrin-like receptors. The simulated cell shape changes in this process and results in a mechanically equilibrated structure with traction and compression forces, in interaction with the substrate reactions. This leads to a compressive microtubule network and a corresponding tensile actin-filament network. The results provide coherent shape and forces information for developing a mechanical model of the cytoskeleton structure, which can be exploitable in future biomechanical studies of adherent cells.

Design and Analysis of a Foldable/Unfoldable Corrugated Architectural Curved Envelop

Origami and paperfolding techniques may inspire the design of structures that have the ability to be folded and unfolded: their geometry can be changed from an extended, servicing state to a compact one, and back-forth. In traditional origami, folds are introduced in a sheet of paper (a developable surface) for transforming its shape, with artistic, or decorative intent; in recent times the ideas behind origami techniques were transferred in various design disciplines to build developable foldable/unfoldable structures, mostly in aerospace industry (Miura, 1985, “Method of Packaging and Deployment of Large Membranes in Space,” Inst. Space Astronaut. Sci. Rep., 618 , pp. 1–9; Ikema , 2009, “Deformation Analysis of a Joint Structure Designed for Space Suit With the Aid of an Origami Technology,” 27th International Symposium on Space Technology and Science (ISTS)). The geometrical arrangement of folds allows a folding mechanism of great efficiency and is often derived from the buckling patterns of simple geometries, like a plane or a cylinder (e.g., Miura-ori and Yoshimura folding pattern) (Wu , 2007, “Optimization of Crush Characteristics of the Cylindrical Origami Structure,” Int. J. Veh. Des., 43 , pp. 66–81; Hunt and Ario, 2005, “Twist Buckling and the Foldable Cylinder: An Exercise in Origami,” Int. J. Non-Linear Mech., 40 (6), pp. 833–843). Here, we interest ourselves to the conception of foldable/unfoldable structures for civil engineering and architecture. In those disciplines, the need for folding efficiency comes along with the need for structural efficiency (stiffness); for this purpose, we will explore nondevelopable foldable/unfoldable structures: those structures exhibit potential stiffness because, when unfolded, they cannot be flattened to a plane (nondevelopability). In this paper, we propose a classification for foldable/unfoldable surfaces that comprehend non fully developable (and also non fully foldable) surfaces and a method for the description of folding motion. Then, we propose innovative geometrical configurations for those structures by generalizing the Miura-ori folding pattern to nondevelopable surfaces that, once unfolded, exhibit curvature.

Selfstress States Identification and Localization in Modular Tensegrity Grids

The design of a modular tensegrity grid requires the determination of its selfstress states, before choosing an appropriate combination defining the systems initial stresses. However, the computation of the vectorial basis associated with selfstress states generally produces results that are difficult to exploit. We therefore propose two different strategies to identify and localize selfstress states in a modular tensegrity grid more pertinently. The first is based on a heuristic approach that exploits the systems structural composition of modularity and regularity. The second is numerical and aims at redefining the vectors of the basis in a more convenient and useful way. Two methods based on transformations of the vectorial basis of selfstress states have been developed for a minimal number of involved components. Finally, we suggest a selfstress state classification based on the number of components and their localization as well as on their mechanical behavior.

Cutting Pattern of Fabric Membranes with the Stress Composition Method

Study of fabric membranes emphasises on numerous difficulties which have to be overcome according to the willingness of reducing errors. We meet hence the first step of form-finding which must be achieved such as it ensures the determination of tensile shapes characterised by the lack of compressive areas. Therefore, it implies the knowledge of both the whole geometry and the prestress tensor at each point of the surface. Nevertheless, these considerations may be regarded as theoretical ones since the designer must then focus on the realisation of the membrane, in other words, on the determination the plane fabric strips which once assembled together and placed into position in space with anchorage points define the required configuration. This paper thus describes a new method devoted to the calculation of the strips with the aim of overcoming the drawbacks of the traditional processes. The used mechanical approaches allow to reduce distortions and errors by taking into account the whole geometrical characteristics of the strip, its stress distribution and the material constitutive laws. The theoretical formulation associates the operations of development and reduction and is based upon an iterative numerical procedure which converges to appropriate plane strips where distortions are minimised by least square methods. Several illustrative applications point out the efficiency of the method.

Visual spatial learning of complex object morphologies through the interaction with virtual and real-world data

Conceptual design relies on extensive manipulation of the morphological properties of real or virtual objects. This study aims to investigate the nature of the perceptual information that could be retrieved in different representation modalities to learn a complex structure. An abstract and complex object was presented to two study populations, experts and non-experts, in three different representation modalities: 2D view; digital 3D model; real object. After viewing, observers had to draw some parts of the structure into a 2D reference frame. The results reveal a considerable performance advantage of digital 3D compared with real 3D, especially in the expert population. The results are discussed in terms of the nature of the morphological cues made available in the different representation modalities.

Conceptual Design and Analysis of a Deployable Structure with Flexible Joints

The conceptual design of a self-deployable structure with flexible joints is presented in this paper. Joints store elastic energy in the folded, prestressed position and allow deployment until they are stopped by tendons. A study on a wire rope joint is first presented to determine its mechanical behavior with experimental, theoretical, and numerical approaches. An analysis is then performed on a bidimensional structure to propose the specific modeling of introducing prestress to the joints. The method is applied to a spatial system in an analysis that uses static equilibrium and kinematic deployment simulations. The results show good concordance among the different approaches.

Investigation of minimal forms with conjugate gradient method

Abstract Amongst the numerous calculation methods available to investigate minimal forms, an approach based on the mechanical consideration of uniform tension in the domain leads to the writing of innovative relationships. Indeed, by establishing the equivalence between the vector of nodal internal forces due to the prestressed domain and the gradient of the function to be minimized, this study proposes to use the conjugate gradient method as a minimal area shape form-finding tool. The determination of descent directions may refer to Fletcher–Reeves suggestion or to an optimized value based on the Polak–Ribiere formula. Moreover, the steplength calculation is envisaged in accordance with the More and Thuentes line search algorithm or with a modified approach especially adapted to the studied configurations. Numerical experiments illustrate the use of the conjugate gradient method and thus point out the efficiency of the suggested modifications related to required computation times. In a second time, the conjugate gradient method is compared with density methods and a mixed formulation is therefore put forward. Numerical tests enable the comparison between these different approaches.

Structural Morphology Issues in Conceptual Design of Double Curved Systems

Non-standard architecture is generally defined by complex double curved systems. We described in this paper three morphogenesis processes. Analytic forms are mainly characterized by regular geometries like cylinders or spheres and portions of these geometric forms are present throughout the history of architecture. Mechanical forms appeared mainly during the second half of the twentieth century, under the impetus of pioneers like Frei Otto: These shapes are guided by an equilibrium condition, the expression of which is known as “form-finding”. Funicular, prestressed and self stressed systems are clearly in this second class. Initiated by the so-called “Bilbao effect” a new trend of double curved systems appeared, characterized by complete free forms that we name flexible forms. The objective is to analyse these classes of forms in relation with parameters of forces, material, technology and structural composition, which are coupled in the conceptual design process. We introduce mainly the coupling between form and structural composition (structural morphology). The last class reveals a lack of links between the parameters, and a complete dislocation of the successive steps of the design process. The evolution from analytical forms to flexible forms, via mechanically-constrained forms is examined in order to determine which constraints designers faced either due to their own choice or for other causes.

The Non-Proliferative Nature of Ascidian Folliculogenesis as a Model of Highly Ordered Cellular Topology Distinct from Proliferative Epithelia

Previous studies have addressed why and how mono‐stratified epithelia adopt a polygonal topology. One major additional, and yet unanswered question is how the frequency of different cell shapes is achieved and whether the same distribution applies between non-proliferative and proliferative epithelia. We compared different proliferative and non-proliferative epithelia from a range of organisms as well as Drosophila melanogaster mutants, deficient for apoptosis or hyperproliferative. We show that the distribution of cell shapes in non‐proliferative epithelia (follicular cells of five species of tunicates) is distinctly, and more stringently organized than proliferative ones (cultured epithelial cells and Drosophila melanogaster imaginal discs). The discrepancy is not supported by geometrical constraints (spherical versus flat monolayers), number of cells, or apoptosis events. We have developed a theoretical model of epithelial morphogenesis, based on the physics of divided media, that takes into account biological parameters such as cell‐cell contact adhesions and tensions, cell and tissue growth, and which reproduces the effects of proliferation by increasing the topological heterogeneity observed experimentally. We therefore present a model for the morphogenesis of epithelia where, in a proliferative context, an extended distribution of cell shapes (range of 4 to 10 neighbors per cell) contrasts with the narrower range of 5-7 neighbors per cell that characterizes non proliferative epithelia.