Computational morphogenesis of free form shells: Filter methods to create alternative solutions

p. 536-547Actual trends in numerical shape optimal design of structures deal with handling of very large dimensions of design space. The goal is to allowing as much design freedom as possible while considerably reducing the modelling effort. As a consequence, several technical problems have to be solved to get procedures which are robust, easy to use and which can handle many design parameters efficiently. The paper briefly discusses several of the most important aspects in this context and presents many illustrative examples which show typical applications for the design of light weight shell and membrane structures.Bletzinger, K.; Firi, M.; Linhard, J.; Wüchner, R. (2009). Computational morphogenesis of free form shells: Filter methods to create alternative solutions. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654

Geometric Construction-Based Realization of Spatial Elastic Behaviors in Parallel and Serial Manipulators

This paper addresses the realization of spatial elastic behavior with a parallel or a serial manipulator. Necessary and sufficient conditions for a manipulator (either parallel or serial) to realize a specific elastic behavior are presented and interpreted in terms of the manipulator geometry. These conditions completely decouple the requirements on component elastic properties from the requirements on mechanism kinematics. New construction-based synthesis procedures for spatial elastic behaviors are developed. With these synthesis procedures, one can select each elastic component of a parallel (or serial) mechanism based on the geometry of a restricted space of allowable candidates. With each elastic component selected, the space of allowable candidates is further restricted. For each stage of the selection process, the geometry of the remaining allowable space is described

Controlling cell-matrix traction forces by extracellular geometry

We present a minimal continuum model of strongly adhering cells as active contractile isotropic media and use the model to study the effect of the geometry of the adhesion patch in controlling the spatial distribution of traction and cellular stresses. Activity is introduced as a contractile, hence negative, spatially homogeneous contribution to the pressure. The model shows that patterning of adhesion regions can be used to control traction stress distribution and yields several results consistent with experimental observations. Specifically, the cell spread area is found to increase with substrate stiffness and an analytic expression for the dependence is obtained for circular cells. The correlation between the magnitude of traction stresses and cell boundary curvature is also demonstrated and analyzed.Comment: 12 pages, 4 figure

A jigsaw puzzle framework for homogenization of high porosity foams

An approach to homogenization of high porosity metallic foams is explored. The emphasis is on the \Alporas{} foam and its representation by means of two-dimensional wire-frame models. The guaranteed upper and lower bounds on the effective properties are derived by the first-order homogenization with the uniform and minimal kinematic boundary conditions at heart. This is combined with the method of Wang tilings to generate sufficiently large material samples along with their finite element discretization. The obtained results are compared to experimental and numerical data available in literature and the suitability of the two-dimensional setting itself is discussed.Comment: 11 pages, 7 figures, 3 table

Comments on “The Principal Axes Decomposition of Spatial Stiffness Matrices”

A significant amount of research has been directed toward developing a more intuitive appreciation of spatial elastic behavior. Results of these analyses have been described in terms of behavior decompositions and in terms of behavior centers. In a recent paper entitled “The Principal Axes Decomposition of Spatial Stiffness Matrices” by Chen et al. (IEEE Trans. Robot., vol. 31, no. 1, pp. 191-207), a decomposition of spatial stiffness was presented, and centers of stiffness and compliance were identified. The results presented in the paper have substantial overlap with previously published results and redefine previously used terms. The objective of this communication is to clarify the contributions of prior work and to standardize the terminology used in describing spatial elastic behavior

A novel model for one-dimensional morphoelasticity. Part II - Application to the contraction of fibroblast-populated collagen lattices

Fibroblast-populated collagen lattices are commonly used in experiments to study the interplay between fibroblasts and their pliable environment. Depending on the method by which\ud they are set, these lattices can contract significantly, in some cases contracting to as little as 10% of their initial lateral (or vertical) extent. When the reorganisation of such lattices by fibroblasts is interrupted, it has been observed that the gels re-expand slightly but do not return to their original size. In order to describe these phenomena, we apply our theory of one-dimensional morphoelasticity derived in Part I to obtain a system of coupled ordinary differential equations, which we use to describe the behaviour of a fibroblast-populated collagen lattice that is tethered by a spring of known stiffness. We obtain approximate solutions that describe the behaviour of the system at short times as well as those that are valid for long times. We also obtain an exact description of the behaviour of the system in the case where the lattice reorganisation is interrupted. In addition, we perform a perturbation analysis in the limit of large spring stiffness to obtain inner and outer asymptotic expansions for the solution, and examine the relation between force and traction stress in this limit. Finally, we compare predicted numerical values for the initial stiffness and viscosity of the gel with corresponding values for previously obtained sets of experimental data and also compare the qualitative behaviour with that of our model in each case. We find that our model captures many features of the observed behaviour of fibroblast-populated collagen lattices

Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations

Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to large number of spatial grid points. For multidimensional reaction-diffusion equations, stiffness of the system provides additional challenges for achieving efficient numerical simulations. In this paper, we propose a class of Krylov implicit integration factor (IIF) discontinuous Galerkin (DG) methods on sparse grids to solve reaction-diffusion equations on high spatial dimensions. The key ingredient of spatial DG discretization is the multiwavelet bases on nested sparse grids, which can significantly reduce the numbers of degrees of freedom. To deal with the stiffness of the DG spatial operator in discretizing reaction-diffusion equations, we apply the efficient IIF time discretization methods, which are a class of exponential integrators. Krylov subspace approximations are used to evaluate the large size matrix exponentials resulting from IIF schemes for solving PDEs on high spatial dimensions. Stability and error analysis for the semi-discrete scheme are performed. Numerical examples of both scalar equations and systems in two and three spatial dimensions are provided to demonstrate the accuracy and efficiency of the methods. The stiffness of the reaction-diffusion equations is resolved well and large time step size computations are obtained