


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, nonlinear 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 pathfollowing 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.
Pathfollowing strategies
The goal of research is a robust formulation of the pathfollowing 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 pathfollowing 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.
Multimodal 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
postcritical 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 branchandcut 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 2D ealstoplastic solids, postcritical 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 6nodes and an 8nodes 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 elastoplastic solids. The variational formulation
of the mixed element has been enriched with the weak statement of the KuhnTucker plastic conditions. The elastoplastic
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 elastoplastic plates subjected to loads normal to
the middle plane.


Boundary element models


Elastoplastic analysis using boundary elements
When material nonlinearity 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 elastoplasticity following an initialstress approach. Each line of the
crosssection is treated as a 'macroelement' with a Bspline interpolation. In next future
we're going to apply those strategies to damage mechanics.



Torsion and flexure analysis of composite beam
The SaintVenant torsion and flexure analysis for a general crosssection 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 crosssection. 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
multimaterial beams. Each line of the crosssection is treated as a 'macroelement' with a Bspline 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 crosssection (torsional stiffness, shear center location,...),
shearstresses 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
Download .xls file


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 illconditioning 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 illconditoned problem has been tackled with
a MonteCarlo 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 nondestructive 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


DiscontinuousGalerkin 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 DiscontinuousGalerkin 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 flatshell structures.


Masonry structures


FEM models and multilevel 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.
