Lluís Gil

Shape and cross-section optimisation of a truss structure

Abstract This article presents a method for the identification of the optimum shape and cross-sections of a plane truss structure under stress and geometrical constraints. The shape design problem is defined by the unknown nodal co-ordinates and is combined with a parametric design problem defined by the cross-sections. The method includes a new approach to merge these two problems and thus resolves the difficulties that arise when combining the optimisation of variables of such different nature. The methodology combines a full stress design optimisation with a conjugates gradient optimisation. The results are compared to steel bridge constructions built at the beginning of the century, when saving material was of great importance.

Temnospondyli bite club: ecomorphological patterns of the most diverse group of early tetrapods

Temnospondyls were a successful group of early tetrapods that lived during the Palaeozoic and Mesozoic periods. Different ecomorphotypes were present (terrestrial, amphibious and fully aquatic) with a wide range of lifestyles. Herein, we analysed several clades of temnospondyls using geometric morphometrics, Finite Element Analysis, and comparative phylogenetic analysis. Some temnospondyli clades were ‘crocodilomorph’ feeding analogues. The skull analysis reveals a concordance between form and feeding function, in amphibious and fully aquatic feeders. The form of terrestrial feeders could be consequences of adaptative or phylogenetical constraints. Basal temnospondyls, as edopoids, were able to leave the water and feed on land. Eryopids continued as terrestrial feeders, although some members showed a shift to increased aquatic feeding. The aquatic environment was especially occupied by archegosaurs during the Permian. After the Permo‐Triassic extinction, trematosaurs and capitosaurs returned to the aquatic environment and their members were amphibious and fully aquatic feeders until their disappearance.

Structural shape sensitivity analysis for nonlinear material models with strain softening

This paper describes some considerations around the analytical structural shape sensitivity analysis when the structural behaviour is computed using the finite element method with a nonlinear constitutive material model. Traditionally, the structural sensitivity analysis is computed using an incremental approach based on the incremental procedures for the solution of the structural equilibrium problem. In this work, a direct (nonincremental) formulation for computing these structural sensitivities, that is valid for some specific nonlinear material models, is proposed. The material models for which the presented approach is valid are characterized by the fact that the stresses at any timet can be expressed in terms of the strains at the timet and, in some cases, the strains at a specific past timetu (tu<t). This is the case of elasticity (linear as well as nonlinear), perfect plasticity and damage models. A special strategy is also proposed for material models with strain softening.For the cases where it is applicable, the sensitivity analysis proposed here allows us to compute the structural sensitivities around any structural equilibrium point after finishing the solution process and it is completely independent of the numerical scheme used to solve the structural equilibrium problem. This possibility is particularized for the case of a damage model considering a strain-softening behaviour. Finally, the quality and reliability of the proposed approach is assessed through its application to some examples.

Skull Mechanics and the Evolutionary Patterns of the Otic Notch Closure in Capitosaurs (Amphibia: Temnospondyli)

Capitosaurs were among the largest amphibians that have ever lived. Their members displayed an amphibious lifestyle. We provide new information on functional morphology data, using finite element analysis (FEA) which has palaeoecological implications for the group. Our analyses included 17 taxa using (2D) plate models to test four loading cases (bilateral, unilateral and lateral bitings and skull raising system simulation). Our results demonstrates that, when feeding, capitosaurs concentrated the stress at the circumorbital region of the capitosaur skull and cranial sutures probably played a key role in dissipating and absorbing the stress generated during biting. Basal members (as Wetlugasaurus) were probably less specialized forms, while during Middle‐ and Late Triassic the group radiated into different ecomorphotypes with closed otic notch forms (as Cyclotosaurus) resulting in the strongest skulls during biting. Previous interpretations discussed a trend from an open to closed otic notch associated with lateral repositioning of the tabular horns, but the analysis of the skull‐raising system reveals that taxa exhibiting posteriorly directed tabular horns display similar results during skull raising to those of closed otic notch taxa. Our results suggest that various constraints besides otic notch morphology, such as the elongation of the tabular horns, snout length, skull width and position, and size of the orbits affect the function of the skull. On the light of our results, capitosaur skull showed a trend to reduce the stresses and deformation during biting. Capitosaurs could be considered crocodilian analogues as they were top‐level predators in fluvial and brackish Triassic ecosystems. Anat Rec, , 2012.

Comparative 3D analyses and palaeoecology of giant early amphibians (Temnospondyli: Stereospondyli)

Macroevolutionary, palaeoecological and biomechanical analyses in deep time offer the possibility to decipher the structural constraints, ecomorphological patterns and evolutionary history of extinct groups. Here, 3D comparative biomechanical analyses of the extinct giant early amphibian group of stereospondyls together with living lissamphibians and crocodiles, shows that: i) stereospondyls had peculiar palaeoecological niches with proper bites and stress patterns very different than those of giant salamanders and crocodiles; ii) their extinction may be correlated with the appearance of neosuchians, which display morphofunctional innovations. Stereospondyls weathered the end-Permian mass extinction, re-radiated, acquired gigantic sizes and dominated (semi) aquatic ecosystems during the Triassic. Because these ecosystems are today occupied by crocodilians, and stereospondyls are extinct amphibians, their palaeobiology is a matter of an intensive debate: stereospondyls were a priori compared with putative living analogous such as giant salamanders and/or crocodilians and our new results try to close this debate.

The virtual laboratory concept applied to strain measurements

In recent years the methodology of engineering education has been changing and many projects deal with improving the educational software. This paper reports on the virtual laboratory, a virtual environment applied to experimental analysis. The goals of the virtual laboratory are to introduce the laboratory environment to the student entering this world, so different from the typical theoretical lectures, for the first time, and to overcome the above-mentioned drawbacks. It should be mentioned that the virtual laboratory is not meant to replace highly enriching, practical experience, but rather is meant to train the individual, in order to improve his/her performance in later actual practice. The virtual laboratory experience starts with the study of strain measurements, an engineering technique widely used to measure deformations, strains, mechanical properties of materials and other variables which are used to analyse many problems.The strain measurement virtual laboratory is meant to offer the possibility of simulating experiences, undergone in a real laboratory, through the Internet. The student is expected to familiarize him/herself with the techniques, procedures, devices and theories in the laboratory environment.

Insights into the controversy over materials data for the comparison of biomechanical performance in vertebrates

Mechanical comparison of different species is performed with the help of computational tools like Finite Element Analysis FEA. In palaeobiology it is common to consider bone like an isotropic material for simulations but often real data of bone materials is impossible to know. This work investigates the influence of choice of bone materials properties over the results of simulations, showing when and why the materials data are relevant and when the selection of these data becomes irrelevant. With a theoretical approach from continuum mechanics and with a practical example the relationship between material data and comparative metrics like stress, strains and displacements is discussed. When linear and elastic material properties are assumed in a comparative analysis, the effect of the elastic modulus of the material is irrelevant over stress patterns. This statement is true for homogeneous and inhomogeneous materials, in this last case the proportion between the different materials properties must kept constant. In the case of the strains and displacements, there is an inverse proportionality kept constant, between the values of the metrics and the changes in the elastic modulus. These properties allow comparative studies without considering the real elastic materials properties.

3D Computational Mechanics Elucidate the Evolutionary Implications of Orbit Position and Size Diversity of Early Amphibians

For the first time in vertebrate palaeontology, the potential of joining Finite Element Analysis (FEA) and Parametrical Analysis (PA) is used to shed new light on two different cranial parameters from the orbits to evaluate their biomechanical role and evolutionary patterns. The early tetrapod group of Stereospondyls, one of the largest groups of Temnospondyls is used as a case study because its orbits position and size vary hugely within the members of this group. An adult skull of Edingerella madagascariensis was analysed using two different cases of boundary and loading conditions in order to quantify stress and deformation response under a bilateral bite and during skull raising. Firstly, the variation of the original geometry of its orbits was introduced in the models producing new FEA results, allowing the exploration of the ecomorphology, feeding strategy and evolutionary patterns of these top predators. Secondly, the quantitative results were analysed in order to check if the orbit size and position were correlated with different stress patterns. These results revealed that in most of the cases the stress distribution is not affected by changes in the size and position of the orbit. This finding supports the high mechanical plasticity of this group during the Triassic period. The absence of mechanical constraints regarding the orbit probably promoted the ecomorphological diversity acknowledged for this group, as well as its ecological niche differentiation in the terrestrial Triassic ecosystems in clades as lydekkerinids, trematosaurs, capitosaurs or metoposaurs.

Finite Element Comparison of 10 Orthodontic Microscrews with Different Cortical Bone Parameters

PURPOSE Unlike standard dental implants, the stabilization of orthodontic microscrews removed after treatment is done without osseointegration and achieved by several components: cortical bone thickness (CBT), microscrew geometry, and drilling depth. The purpose of this study was to evaluate 10 different microscrews and the influence of their geometric parameters with different CBT and drilling depths. MATERIALS AND METHODS The influence of geometric parameters in cortical bone was analyzed with a series of computational simulations with finite element models to obtain von Mises stresses and deformations in the microscrew when loaded with a perpendicular traction force of 1 N and considering the angle of incidence as a random parameter. RESULTS There was variability in the angle of incidence, with less clinical influence. Biomechanical parameters such as microscrew diameter, CBT, and drilling depth had significant influences on the results. At a drilling distance of 8 mm, narrow microscrews (Abso Anchor 1.2) showed maximum von Mises stress of 500.698 MPa and maximum deformation in the shank of 0.08549 mm. Microscrews with a diameter of 1.5 mm (Dentaurum, Jeil, Mondeal, Tekka, Spider) showed von Mises stresses ranging from 56.97 to 136 MPa and deformation between 0.0062055 and 0.0476 mm. Microscrews with a diameter of 2.0 mm (Jeil, Mondeal, Tekka) showed von Mises stresses ranging from 17.172 to 54.861 MPa and deformation of 0.000172 to 0.0161 mm. CONCLUSIONS The shape and geometry of an orthodontic microscrew are highly important in its behavior. Optimal characteristics of a microscrew would include a diameter of 2.0 mm, a cylindric shape, a short and wide head, a short and wide shank, and threads of an appropriate size.

Bending performance of concrete beams strengthened with textile reinforced mortar TRM

This work presents a method of strengthening concrete structures based on textiles of high strength and mortars. The combination of textiles and mortars produces a new composite material with cementitious matrix. This material can be used for the reinforcement of concrete beams under bending loads. We tested several combinations of fibers: glass, Poliparafenil Benzobisoxazol (PBO), steel and carbon fibers with mortar and we used them to reinforce precast concrete beams. All the specimens were tested with a four-point load test. We discuss the performance of the specimens and we compare the ultimate results with the formulae from FRP codes.