Luciano Lamberti

Move limits definition in structural optimization with sequential linear programming. Part I: Optimization algorithm

Abstract A variety of numerical methods have been proposed in literature in purpose to deal with the complexity and non-linearity of structural optimization problems. In practical design, sequential linear programming (SLP) is very popular because of its inherent simplicity and because linear solvers (e.g. Simplex) are easily available. However, SLP performance is sensitive to the definition of proper move limits for the design variables which task itself often involves considerable heuristics. This research presents a new SLP algorithm (LESLP––linearization error sequential linear programming) that implements an advanced technique for defining the move limits. The LESLP algorithm is formulated so to overcome the traditional limitations of the SLP method. The new algorithm is successfully tested in weight minimization problems of truss structures with up to hundreds of design variables and thousands of constraints: sizing and configuration problems are considered. Optimization problems of non-truss structures are also presented. The key-ideas of LESLP and the discussion on numerical efficiency of the new algorithm are presented in a two-part paper. The first part concerns the basics of the LESLP formulation and provides potential users with a guide to programming LESLP on computers. In a companion paper, the numerical efficiency, advantages and drawbacks of LESLP are discussed and compared to those of other SLP algorithms recently published or implemented in commercial software packages.

Move limits definition in structural optimization with sequential linear programming. Part II: Numerical examples

Abstract A variety of numerical methods have been proposed in literature in purpose to deal with the complexity and non-linearity of structural optimization problems. In practical design, sequential linear programming (SLP) is very popular because of its inherent simplicity and because linear solvers (e.g. Simplex) are easily available. However, SLP performance is sensitive to the definition of proper move limits for the design variables which task itself often involves considerable heuristics. This research presents a new SLP algorithm (LESLP) that implements an advanced technique for defining the move limits. The linearization error sequential linear programming (LESLP) algorithm is formulated so to overcome the traditional limitations of the SLP method. In a companion paper [Comput. Struct. 81 (2003) 197] the basics of the LESLP formulation along with a guide to programming are provided. The new algorithm is successfully tested in weight minimisation problems of truss structures with up to hundreds of design variables and thousands of constraints: sizing and configuration problems are considered. Optimization problems of non-truss structures are also presented. The numerical efficiency, advantages and drawbacks of LESLP are discussed and compared to those of other SLP algorithms recently published or implemented in commercial software packages.

Nanoscale characterization of the biomechanical hardening of bovine zona pellucida

The zona pellucida (ZP) is an extracellular membrane surrounding mammalian oocytes. The so-called zona hardening plays a key role in fertilization process, as it blocks polyspermy, which may also be caused by an increase in the mechanical stiffness of the ZP membrane. However, structural reorganization mechanisms leading to ZPs biomechanical hardening are not fully understood yet. Furthermore, a correct estimate of the elastic properties of the ZP is still lacking. Therefore, the aim of the present study was to investigate the biomechanical behaviour of ZP membranes extracted from mature and fertilized bovine oocytes to better understand the mechanisms involved in the structural reorganization of the ZP that may lead to the biomechanical hardening of the ZP. For that purpose, a hybrid procedure is developed by combining atomic force microscopy nanoindentation measurements, nonlinear finite element analysis and nonlinear optimization. The proposed approach allows us to determine the biomechanical properties of the ZP more realistically than the classical analysis based on Hertzs contact theory, as it accounts for the nonlinearity of finite indentation process, hyperelastic behaviour and material heterogeneity. Experimental results show the presence of significant biomechanical hardening induced by the fertilization process. By comparing various hyperelastic constitutive models, it is found that the Arruda–Boyce eight-chain model best describes the biomechanical response of the ZP. Fertilization leads to an increase in the degree of heterogeneity of membrane elastic properties. The Young modulus changes sharply within a superficial layer whose thickness is related to the characteristic distance between cross-links in the ZP filamentous network. These findings support the hypothesis that biomechanical hardening of bovine ZP is caused by an increase in the number of inter-filaments cross-links whose density should be higher in the ZP inner side.

Comparison of the numerical efficiency of different sequential linear programming based algorithms for structural optimisation problems

Abstract Amongst the different optimisation methods, the Sequential Linear Programming (S.L.P.) is very popular because of its conceptual simplicity and of the large availability of LP commercial packages (i.e. Simplex algorithm). Unfortunately, the numerical efficiency of the S.L.P. method depends meaningfully on a proper choice of the move limits that are adopted for the optimisation variables. In this paper the effect on the numerical solution of different move limits definition criteria has been investigated. Two different approaches (CGML and LEAML) for the definition of the move limits in Sequential Linear Programming are described and compared in terms of numerical efficiency in the solution of six problems of weight minimisation of bar trusses structures.

Comparison of different orthodontic devices for mandibular symphyseal distraction osteogenesis: A finite element study

INTRODUCTION In this study, we aimed to analyze the displacement field and the level of stability for a human mandible that had symphyseal distraction osteogenesis. The mandible was fitted with various orthodontic devices: tooth borne, bone borne, and hybrid. Three-dimensional nonlinear finite element analyses were performed to study differences between the nominal aperture of the device and the actual mandibular distraction. Furthermore, displacement fields of the mandibular arch evaluated with and without mastication forces were compared to determine the level of stability of each appliance. METHODS Computed tomography scan images of the mandible were processed to create the finite element model, which was completed by modeling the distraction device. Three cases were considered: the distraction device attached to the first molar and the first premolar (tooth borne), to the canine and basal bones (hybrid), or only to the basal bone (bone borne). The nominal aperture of each device was 2 mm. Mandibular displacements in the mastication phase were analyzed in the case of unilateral occlusion on the second premolar. RESULTS AND CONCLUSIONS Tooth-borne and hybrid devices allow orthodontists to better control the effective displacement transferred to the mandible by the distractor. Displacements of the mandibular arch were closer to the nominal aperture of the distractor than in the case of the bone-borne device. Hybrid devices were more stable under functional loads. However, parasitic rotations of the mandibular arms caused by mastication might counteract the benefits of distraction.

Whole-Depth Change in Bovine Zona Pellucida Biomechanics after Fertilization: How Relevant in Hindering Polyspermy?

Polyspermy is a common problem in bovine in vitro fertilization (IVF) and has a still unclear etiology. In this specie, after IVF, despite the lack of a biochemical post-fertilization hardening, the stiffness of the outer ZP layer is significantly increased. Therefore, polyspermy might be related to an incomplete or insufficient stiffening of the ZP. We obtained, by using atomic force spectroscopy in physiological conditions, a complete characterization of the biomechanical changes of the inner and outer ZP layers occurring during oocyte maturation/fertilization and correlated them to the ultrastructural changes observed by transmission electron microscopy using ruthenium red and saponin technique. In both the inner and outer ZP layers, stiffness decreased at maturation while, conversely, increased after fertilization. Contextually, at the nanoscale, during maturation both ZP layers displayed a fine filaments network whose length increased while thickness decreased. After fertilization, filaments partially recovered the immature features, appearing again shorter and thicker. Overall, the observed biomechanical modifications were substantiated by ultrastructural findings in the ZP filament mesh. In fertilized ZP, the calculated force necessary to displace ZP filaments resulted quite similar to that previously reported as generated by bovine sperm flagellum. Therefore, in bovine IVF biomechanical modifications of ZP appear ineffective in hindering sperm transit, highlighting the relevance of additional mechanisms operating in vivo.

High-accuracy contouring using projection moiré

Shadow and projection moire are the oldest forms of moire to be used in actual technical applications. In spite of this fact and the extensive number of papers that have been published on this topic, the use of shadow moire as an accurate tool that can compete with alternative devices poses very many problems that go to the very essence of the mathematical models used to obtain contour information from fringe pattern data. In this paper some recent developments on the projection moire method are presented. Comparisons between the results obtained with the projection method and the results obtained by mechanical devices that operate with contact probes are presented. These results show that the use of projection moire makes it possible to achieve the same accuracy that current mechanical touch probe devices can provide.

A Mechanobiology-based Algorithm to Optimize the Microstructure Geometry of Bone Tissue Scaffolds

Complexity of scaffold geometries and biological mechanisms involved in the bone generation process make the design of scaffolds a quite challenging task. The most common approaches utilized in bone tissue engineering require costly protocols and time-consuming experiments. In this study we present an algorithm that, combining parametric finite element models of scaffolds with numerical optimization methods and a computational mechano-regulation model, is able to predict the optimal scaffold microstructure. The scaffold geometrical parameters are perturbed until the best geometry that allows the largest amounts of bone to be generated, is reached. We study the effects of the following factors: (1) the shape of the pores; (2) their spatial distribution; (3) the number of pores per unit area. The optimal dimensions of the pores have been determined for different values of scaffold Youngs modulus and compression loading acting on the scaffold upper surface. Pores with rectangular section were predicted to lead to the formation of larger amounts of bone compared to square section pores; similarly, elliptic pores were predicted to allow the generation of greater amounts of bone compared to circular pores. The number of pores per unit area appears to have rather negligible effects on the bone regeneration process. Finally, the algorithm predicts that for increasing loads, increasing values of the scaffold Youngs modulus are preferable. The results shown in the article represent a proof-of-principle demonstration of the possibility to optimize the scaffold microstructure geometry based on mechanobiological criteria.

Challenges in comparing numerical solutions for optimum weights of stiffened shells

Optimizations of stiffened shells with different stiffener shapes performed to rank and identify the optimum designs during the preliminary design trade studies require a large number of analyses and hence rely on the useof efficient but approximate analysis methods. In the design of shells, the treatment of imperfections on buckling loads and stresses is of paramount importance. It is demonstrated how conservativeness of the approximate analyses used in buckling load calculation, the number of variables optimized (design freedom), and nonstructural constraints influence the weight of optimum designs. This demonstration is based on the results of a trade study performed to compare minimum weight designs of stiffened shells optimized under stress and buckling constraints for a reusable launch vehicle tank. PANDA2 was selected for the present study because it uses approximate analysis procedures that permit the many thousands of structural analyses needed for global optimization and it also has sophisticated machinery for generating imperfections and accounting for their effects. Optimum weights were influenced not only by material choice, number of optimization variables, and manufacturing constraints, but also by the analysis model conservativeness. Optimization of shells with effect of initial imperfections exhibited substantial weight differences between different stiffened-shell concepts, partly because of conservativeness in the analysis.

A New Hybrid Technique for In-plane Characterization of Orthotropic Materials

In this paper we present a novel hybrid procedure for the in-plane mechanical characterization of orthotropic materials. The material identification reverse engineering problem is solved by combining speckle interferometry and numerical optimization. The rationale behind the entire process is the following: for any specimen to be characterized and which has been subjected to some loading condition, it is possible to express the difference between experimental data and analytical/numerical predictions by means of an error function ψ, which depends on the elastic constants of the material. The ψ error will decrease as the elastic constants come close to their target values. Here, we build the ψ function as the difference between the displacement field measured with speckle interferometry and its counterpart computed by means of finite element analysis. Since the ψ function is highly non-linear, it has to be optimized with a global optimization algorithm, which perform a random search in the elastic constants design space. The hybrid material identification process finally allows us to determine values of the elastic constants. In order to prove the feasibility of the present approach, we have determined the in-plane elastic properties of an eight-ply composite laminate (woven fiberglass-epoxy) used as a substrate for printed circuit boards. The results indicate that the procedure proposed in this paper was able to accurately characterize the material under investigation. Remarkably, the elastic constants found by the identification procedure were less than 0.7% different from their target values, while the residual error between the displacements measured by speckle interferometry and those computed at the end of the optimization process was less than 3%.