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Material based models for topology optimization of linear elastic solids with a low volume constraint generate very slender structures composed mainly of bars and beam elements. For this type of structure the value of the buckling critical load becomes one of the most important design criteria and so its control is very important for meaningful practical designs. This paper tries to address this problem, presenting an approach to introduce the possibility of critical load control into the topology optimization model.Using the material based formulation for topology design of structures, the problem of optimal structural reinforcement for a critical load criterion is formulated. The stability problem is conveniently reduced to a linearized eigenvalue problem assuming only material effective properties and macroscopic instability modes. The respective optimality criteria are presented by introducing the Lagrangian associated with the optimization problem. Based on this Lagrangian a first-order method is used as a basis for the numerical update scheme. Two numerical examples to validate the developments are presented and analysed.

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Julius Wolff originally proposed that trabecular bone was influenced by mechanical stresses during the formative processes of growth and repair such that trabeculae were required to intersect at right angles. In this work, we have developed an analytical parametric microstructural model, which captures this restriction. Using homogenisation theory, a global material model was obtained. An optimal structure constructed of the homogenised material could then be found by optimising a cost function accounting for both the structural stiffness and the biological cost associated with metabolic maintenance of the bone tissue. The formulation was applied to an example problem of the proximal femur. Optimal densities and orientations were obtained for single load cases. The situation of multiple loads was also considered. In this case, we observe that the alignment of principal strains with the material orthotropy direction is, in general, not possible for all load cases. Thus less restrictive microstructures (nonorthotropic) will yield higher structural stiffnesses than strictly orthotropic microstructures.

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SUMMARYThis paper presents the development of a computational model for the topology optimization problem, using a material distribution approach, of a 2-D linear-elastic solid subjected to thermal loads, with a compliance objective function and an isoperimetric constraint on volume. Defining formally the augmented Lagrangian associated with the optimization problem, the optimality conditions are derived analytically. The results of analysis are implemented in a computer code to produce numerical solutions for the optimal topology, considering the temperature distribution independent of design. The design optimization problem is solved via a sequence of linearized subproblems. The computational model developed is tested in example problems. The influence of both the temperature and the finite element model on the optimal solution obtained is analysed.

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Many tissues are sensitive to mechanical stimuli; however, the mechanotransduction mechanism used by cells remains unknown in many cases. The primary cilium is a solitary, immotile microtubule-based extension present on nearly every mammalian cell which extends from the basal body. The cilium is a mechanosensitive organelle and has been shown to transduce fluid flow-induced shear stress in tissues such as the kidney and bone. The majority of microtubules assemble from the mother centriole (basal body), contributing significantly to the anchoring of the primary cilium. Several studies have attempted to quantify the number of microtubules emanating from the basal body and the results vary depending on the cell type. It has also been shown that cellular response to shear stress depends on microtubular integrity. This study hypothesizes that changing the microtubule attachment of primary cilia in response to a mechanical stimulus could change primary cilia mechanics and, possibly, mechanosensitivity. Oscillatory fluid flow was applied to two different cell types and the microtubule attachment to the ciliary base was quantified. For the first time, an increase in microtubules around primary cilia both with time and shear rate in response to oscillatory fluid flow stimulation was demonstrated. Moreover, it is presented that the primary cilium is required for this loading-induced cellular response. This study has demonstrated a new role for the cilium in regulating alterations in the cytoplasmic microtubule network in response to mechanical stimulation, and therefore provides a new insight into how cilia may regulate its mechanics and thus the cells mechanosensitivity.