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This paper exploits the concept of stabilized finite element methods to formulate stable mixed stress/displacement and strain/displacement finite elements for the solution of nonlinear solid mechanics problems. The different assumptions and approximations used to derive the methods are exposed. The proposed procedure is very general, applicable to 2D and 3D problems and independent of the constitutive equation considered. Implementation and computational aspects are also discussed, showing that a robust application of the proposed formulation is feasible. Numerical examples show that the results obtained compare favourably with those obtained with the corresponding irreducible formulation.

[EN] This work analyzes the influence of the discretization error contained in the Finite Element (FE) analyses of each design configuration proposed by structural shape optimization algorithms over the behaviour of the algorithm. If the FE analyses are not accurate enough, the final solution will neither be optimal nor satisfy the constraints. The need for the use of adaptive FE analysis techniques in shape optimum design will be shown. The paper also proposes the use of the algorithm described in [1] in order to reduce the computational cost associated to the adaptive FE analysis of each geometrical configuration when evolutive optimization algorithms are used.¿, The authors have been sponsored by the Spanish Ministerio de Ciencia e Innovación through the projects DPI2008-05250 (first author) and DPI2007-66773-C02-01 (second and third authors). The second and third authors have also been sponsored by the Generalitat Valenciana and the Universidad Politécnica de Valencia.

In this paper we propose a method to approximate flow problems in moving domains using always a given grid for the spatial discretization, and therefore the formulation to be presented falls within the category of fixed-grid methods. Even though the imposition of boundary conditions is a key ingredient that is very often used to classify the fixed-grid method, our approach can be applied together with any technique to impose approximately boundary conditions, although we also describe the one we actually favor. Our main concern is to properly account for the advection of information as the domain boundary evolves. To achieve this, we use an arbitrary Lagrangian- Eulerian framework, the distinctive feature being that at each time step results are projected onto a fixed, background mesh, that is where the problem is actually solved.

A general statistical framework to perform backanalysis in geotechnical problems from field instrumentation has been presented in a companion paper. Here, an application to a real case involving the excavation of a tunnel in stiff overconsolidated clay is described. Both, extensometer and inclinometer measurements are used as input data and elastic moduli of the ground and the value of the Ko coeficient are estimated. The finite element method is used as the computational procedure to solve the direct problem, and has been coupled to the identification algorithm as described in the companion paper. In addition, a discussion on the reliability of the parameters identified is presented.

This paper deals with the question of strain localization associated with materials which exhibit softening due to tensile straining. A standard local isotropic Rankine damage model with strain-softening is used as exemplary constitutive model. Both the irreducible and mixed forms of the problem are examined and stability and solvability conditions are discussed. Lack of uniqueness and convergence difficulties related to the strong material nonlinearities involved are also treated. From this analysis, the issue of local discretization error in the pre-localization regime is deemed as the main difficulty to be overcome in the discrete problem. Focus is placed on low order finite elements with continuous strain and displacement fields (triangularP1P1and quadrilateralQ1Q1), although the presented approach is very general. Numerical examples show that the resulting procedure is remarkably robust: it does not require the use of auxiliary tracking techniques and the results obtained do not suffer from spurious mesh-bias dependence.

A probabilistic framework to perform inverse analysis of geotechnical problems is presented. The formulation allows the incorporation of existing prior information on the parameters in a consistent way. The method is based on the maximum likelihood approach that allows a straightforward introduction of the error structure of field measurements and prior information. The difficulty of ascribing definite values to the uncertainties associated with the various types of observations is overcome by including the corresponding variances in the set of parameters to be identified. The inverse analysis results in a minimization problem that is solved by coupling the optimization technique to the finite element method. Two examples are presented to illustrate the performance of the method. The first one corresponds to a synthetic case simulating the excavation of a tunnel. Young’s modulus, KO value and measurements variances are identified. The second case concerns the excavation of a large underground cavern in which again Young’s modulus and KO are identified. It is shown that introduction of prior information permits the estimation of parameters more consistent with all available informations that include not only monitored displacements but also results from in situ tests carried out during the site investigation stage.

We present a numerical formulation to compute optical parameters in a turbulent air flow. The basic numerical formulation is a large eddy simulation (LES) of the incompressible Navier-Stokes equations, which are approximated using a finite element method. From the time evolution of the flow parameters we describe how to compute statistics of the flow variables and, from them, the parameters that determine the quality of the visibility. The methodology is applied to estimate the optical quality around telescope enclosures.