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Stategies for structural analysis 
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Research areas

Computational Mechanics field is a scientific area comprehending Mechanics, Numerical Analysis and Computer Sciences and its applications regard all the engineering fields. The activity at labmec mainly concerns structural applications and the computational methodologies regarding FEM and BEM models, analysis of slender structures, non-linear response of materials, inverse problems.


Analysis of slender structures

Koiter analysis

Koiter perturbation method is very suitable for the imperfection sensitivity analysis of elastic slender structures, mainly if the structure is characterized by coincident or nearly coincident buckling modes. The goal of the research activity is to develop reliable FEM models with respect to traditional path-following strategies. To this end a robust and accurate mixed approach was proposed. FEM models based on exact strain measures are the subject of the current activity.

Path-following strategies

The goal of research is a robust formulation of the path-following method which is the reference strategy in the nonlinear analysis of slender structures. Two main guidelines can be devised. 1) Study and development of a strategy based on a mixed formulation of the discrete problem. The resulting algorithm is noteworthy more robust than the standard compatible FEM models. The studied applications are trusses, beam frames and flat shells. 2) Improvement of the predictor phase of the path-following approach by means of efficient extrapolation schemes, obtaining better computational features and more accurate calculations of the equilibrium configurations. The final result is a simpler devising of bifurcation points and definition of the tangent planes to the equilibrium path through local perturbation analyses.

Multi-modal Buckling

In the nonlinear analysis of truss stuctures the local buckling of a discrete number of elements can totally change the global structural response resulting in limit load load lower than the critical load of the overall structure. The problem is tackled with the Koiter asymptotic approach and the attractive paths theory which, among all the post-critical paths of the structure, selects only that ones more important from the mechanical point of view. Than an imperfection sensitivity analysis is performed on the selected modes. The assumption of symmetrical local modes allow the formulation of a not convex quadratic problem. The problem is solved through a recursive branch-and-cut algorithm specifcally implemented for this application. A stochastic study of the collapse load of the structure is also performed on the basis of a imperfection sensitivity analysis with respect to geometrical and load imperfections.


Shakedown analysis

The research is focused on the development of a fem tool to be used in the evaluation of the safety factor with respect to the shakedown condition. The problem is not so simple because the traditional means used in the limit analysis cannot be used for shakedown analysis, as a consequence this kind analysis is not implemented in standard fem codes. The implemented algorithm has been applied to framed structures and 2D solids discretized by standard finite elements.


FEM

HC elements

The High Continuity interpolation is an interpolation technique based on spline functions which allow to obtain an high level of continuity in the description of the unknown field. The resulting discrete model is characterized by reduced computational costs if compared with traditional fem techniques. The formulation has been tested in several engineering contexts: analysis of 2-D ealsto-plastic solids, post-critical analysis of slender panels, boundary elements.

Mixed finite elements

The research is focused on the formulation of high performance finite elements on the basis of a mixed formulation whose main feature is the independent description of the stress field at element level. In the context of 2D solids subjected to plane stress or strain conditions a 6-nodes and an 8-nodes element have been proposed. Always in the same context the use of drilling degrees of freedom have been studied in order to allow the modelling of 3D walled structure.

Mixed formulations has been applied also in the analysis of elasto-plastic solids. The variational formulation of the mixed element has been enriched with the weak statement of the Kuhn-Tucker plastic conditions. The elasto-plastic problem is than formulated and solved at elment level with respect to the stress parameters of the element. Different kinds of element with continuous and dicrete representation of the plastic strain field have been proposed.

Flat elements

Flat elements are very simple triangular elements proposed for the analysis of elasto-plastic plates subjected to loads normal to the middle plane.


Boundary element models

Elasto-plastic analysis using boundary elements

When material non-linearity are involved, the boundary element method needs the use of domain cells and the computation of singular domain integrals. Our research team is developing efficient computation techniques and automatic strategies for the domain cells generation in critical zones. The algorithms have been applied in plane elasto-plasticity following an initial-stress approach. Each line of the cross-section is treated as a 'macro-element' with a B-spline interpolation. In next future we're going to apply those strategies to damage mechanics.

Torsion and flexure analysis of composite beam

The Saint-Venant torsion and flexure analysis for a general cross-section requires a 2D problem to be solved. Dealing with composite beams it is necessary to formulate the problem over each domain, keeping the interface conditions satisfied. Boundary methods have some appealing features which allow an accurate evaluation of the stress field over the cross-section. Advantage can be taken of the easy discretisation process and the possibility of addressing the computational resources to restricted regions of interest. Recently our research team developed a BEM model which is able to perform the torsion and flexure analysis of multi-material beams. Each line of the cross-section is treated as a 'macro-element' with a B-spline interpolation. All the integrals involved have been transferred on the boundary and evalueted in closed form. The computation returns the following output: global characteristics of the cross-section (torsional stiffness, shear center location,...), shear-stresses and warping function distribution.

Finite elements derived from boundary elements

The standard and symmetric boundary integral formulation are used to define a multinode finite element. This finite element is obtained describing the internal displacement and stress fields by Green functions, used as shape functions instead of the usual polynomial approximations. The internal fields are linked to the polynomial functions used to approximate the boundary variables by the relations derived from the Somigliana equation. The proposed approach aims at combining the accuracy of the boundary element discretization with the flexibility in coupling different elements which is typical of energy based models. Two different approaches have been followed to construct such finite elements. The first evaluates the element energy, using a numerical integration of the domain strain energy expressed in terms of the boundary variables. The second is based on the Galerkin method and the related double integration. These models have been coded as numerical procedures for the analysis of plane elasticity problems defined on polygonal domains. Some tests show their numerical performance.

Papers on BEM research

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Inverse problems

Devising boundary conditions for elastic 3D problems

On the basis of a boundary element formulation of a 3D elastic problem, a direct relation between boundary conditions and stress values relative to internal points of the domain has been formulated. The ill-conditioning of the resulting system has been sanitized by using the classical approach of Tikhonov together with the Generalized Cross Validation criterion.

Modelling of applied loads

The experience in the inverse modelling of boundary conditons has been exploited to model also the actions applied on structures. Also in this case the measures of stress in some points of the structures are used to evalute the applied actions. As prototype problem 3D truss structures have been considered. The solution of the resulting ill-conditoned problem has been tackled with a Monte-Carlo strategy for the approximate evaluation of the function which gives the optimal solution.

Structural diagnosis

Useful information regarding defects inside mechanical or structural parts can be obtained through non-destructive electrical or mechanical test. An estimate of the volume of the defect, intended as a portion of the body with different mechanical or electrical properties, can be inferred from measures relative to the boundary of the domain. This procedure allows to minimize and maximize the size of the inclusion. The effectiveness of the method has been verified through numerical parametric studies by using HC finite elements and, because of the huge number of analyses to perform, high performance computational resources.


New computational models

Discontinuous-Galerkin models

The availability of low cost high performance computational resources allows the experimentation of numerical techniques notoriously more expensive with respect to standard models. This is the case of Discontinuous-Galerkin methods whose main feature is the using of interpolation spaces non constrained to be continuous among the element of the discretization. A fem model which can be classified in this family of models has been implemented and tested in order to verify the accuracy and the stability of the formulation. The final aim is to implement this kind of formulation in a parallel context and to apply the method in the analysis of more complex structures such as flat-shell structures.


Masonry structures

FEM models and multi-level strategies for the analysis of complex structures

The modelling of walled or partially framed structures requires an accurate geometrical description capable to represent well also some geometrical details. A computer code which manages different kinds of structural elements has been implemented by solving all the compatibility problems arising during the connection of different elements in a 3D context. Moreover the resulting models are usually very expensive from the computational point of view, as a consenquence standard solution procedures are not effective. To solve this problem an iterative multilevel strategy has been proposed. The different levels are given by discretizations with different coarseness and the reduction of the commputational costs is obtained by an incomplete decomposition technique.

Mixed modelling of damaged orthotropic 2D solids

The research is focused on the formulation of mixed fem models for the analysis of masonry panels. In the context of 2D solids subjected to plane stress condition an orthotropic damage model has been adopted to represent the nonlinear behaviour of regular brickworks. The mixed framework allows the formulation of more effective elements in which the stress parameters are directly linked to the evolution of the assumed damage model.


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Last update: August 2014