An effective Galerkin Boundary Element Method for a 3D half-space subjected to surface loads

In this work, a simple and effective numerical model is proposed for solving the problem of a three-dimensional elastic and isotropic half-space subjected to surface vertical displacements and pressures. For this purpose, the Galerkin Boundary Element Method for a three-dimensional half-space is introduced, and both surface displacement and pressure fields are discretized in order to obtain fast and accurate numerical solution. Assuming a piecewise constant discretization of both surface displacement and pressure fields, several numerical tests are performed showing the effectiveness of the model, for instance by determining accurately the translational and rotational stiffness of a rigid rectangular foundation on elastic half-space, together with the displacements generated by a uniform surface pressure over a rectangular area

Discrete and Continuous Models for Static and Modal Analysis of Out of Plane Loaded Masonry

A critical review of analytical and numerical models for studying masonry out of plane behaviour is presented. One leaf historical masonry, composed by rigid blocks arranged regularly with dry or mortar joints, is considered. Discrete model with rigid blocks, Love-Kirchhoff and Reissner-Mindlin plate models and 3D heterogeneous FEM are adopted. An existing simple and effective discrete model is adopted and improved by applying matrix structural analysis techniques for static and modal analysis of masonry walls in the elastic field, but the formulation allows to account also for material nonlinearity. Elastic parameters of both plate models are based on an existing compatible identification between 3D discrete model and 2D plate models. Static and modal analysis of masonry walls with several boundary conditions are carried on, numerical tests account for in plane size of heterogeneity and structure thickness by means of in and out of plane scale factors. Results show that discrete model is simple and effective for representing masonry behaviour, especially when size of heterogeneity is smaller than overall panel size. Decreasing in plane scale factor, plate models converge to the discrete one, but the Reissner-Mindlin one shows a better convergence and also allows adopting a simple FE for performing numerical analysis

Nonlinear analysis of structures on elastic half-space by a FE-BIE approach

In the present dissertation, a numerical model able to study the non-linear behaviour of structures on elastic half-space is presented. The work takes into account for first the geometric non-linearity of beams and frames on elastic half-plane, namely in plane strain or plane stress condition. This problem is important in many engineering fields and it has been studied in the past by many researchers for the design of sandwich panels in aerospace industry. Recently, this problem has been studied in relation to the buckling of thin films on elastic supports for electronic design. The problem is solved by means of a mixed variational formulation, which assumes as independent fields the displacements of the structure and the contact pressures between foundation and halfspace. The relation between surface displacement and pressure is given by the Flamant solution, which furnishes the half-plane displacement generated by a concentrated force. The second order effects due to axial loads applied on the structure are added to the total potential energy of the system in order to perform buckling analyses. Then, the model is discretized by subdividing the structure into finite elements (FEs) and simplifying contact pressures by a piecewise constant function. Hence, the stationarity conditions of the total potential energy written in discrete form furnish a system of equations which can be solved easily. A soil-structure interaction (SSI) parameter taking into account both the slenderness of the foundation beam and the stiffness of the soil is introduced. The present model was introduced for the first time by Tullini and Tralli (2010) but it was limited to linear elastic analysis. In this case, the model is extended for studying the stability of beams on elastic half-plane, considering both Euler-Bernoulli and Timoshenko beam. In the first chapter, the present model for an Euler-Bernoulli beam on elastic half-plane is compared with a traditional model characterized by the half-space modelled by two-dimensional (2D) FEs. The present model turns out to be efficient and faster than the traditional model. Then, the stability of beams with finite length and with different end restraints is deeply discussed by determining critical loads and the corresponding mode shapes, varying the SSI parameter. Numerical examples are in good agreement with analytic solutions for the case of the beam with sliding ends. Critical loads converge to the values of a beam with infinite length on elastic half-plane and on a set of equidistant supports. The cases of beam with pinned and free ends furnish new estimates of critical loads, which are less than that for the beam with sliding ends and which are characterized by mode shapes with great deflections close to beam ends. In the second chapter, the stability of Timoshenko beams on elastic half-space is discussed. The present model is compared with a traditional model where both beam and half-plane are modelled by 2D FEs. For stiff or quite stiff beams on soft half-plane, the present model is fast and efficient, whereas for slender beams on stiff half-plane, the present model gives critical loads greater than the ones obtained with the traditional model. Differences are caused by the second order effects of the half-plane, which are taken into account in the traditional model. Then, in the third chapter, structures on half-plane are studied taking into account the material nonlinearity for the structure. A lumped plasticity model is considered and flexural plastic hinges are introduced into the discrete model of slender beams and frames on elastic half-plane. For simplicity, a rigid-perfectly plastic moment-rotation relationship is adopted for describing the behaviour of plastic hinges. Material nonlinearity is introduced into the discrete model following an efficient approach adopted for representing semi-rigid connections of frames. The approach gives the possibility to keep the same number of beam FEs and degrees of freedom of the original model, whereas potential plastic hinges are added to beam FE ends by simply modifying the corresponding stiffness matrices. Hence, incremental analyses of beams and frames are performed by placing potential plastic hinges close to concentrated loads and at beam-column connections. In the fourth chapter of the thesis, the discrete model of a beam on elastic half-plane is extended to the three-dimensional case for performing static and buckling analysis of foundation beams. Beams on 3D half-space are important in civil engineering field and they may adopted for representing shallow foundations on elastic soil. In this case, the relation between surface displacements and contact pressure is given by Boussinesq solution. The flexibility matrix of the soil is first determined for solving the Galerkin boundary element method, in order to study the indentation of the half-space by a rigid square punch and determining the displacements generated by uniform pressure distributions over rectangular areas. In both cases, the half-space surface is discretized in both plane directions adopting power graded meshes characterized by very small surface discretizations close to surface edges. Then, Euler-Bernoulli and Timoshenko beams on 3D halfspace subject to different loads are studied and displacements, surface pressures and bending moments are determined. Finally, the stability of Euler-Bernoulli beams on 3D half-space with finite length and different end restraints is considered. Critical loads and mode shapes are similar to those obtained for the 2D case in the fist chapter, however in this case, results are strictly dependent on the ratio between beam length and width

Damage-imperfection indicators for the assessment of multi-leaf masonry walls under different conditions

The complexity of multi-leaf masonry walls suggests further researches on the dy- namic behaviour mainly characterized by incoherent response between the different layers. The intrinsic discontinuity and the manufacturing imperfections are amplified by the incre- mental damage that triggers different failure mechanisms that affect the dynamic parameters, such as modal shapes, frequencies and damping ratios. The dynamic identification with out- put only methodology has been proposed in this work on different multi-leaf masonry walls subjected to uniaxial compressive load. The responses of full infill, damaged infill and strengthened infill masonry panels with different widespread damage have been recorded. The evolution of the damage scenario changes the modal shapes, the related frequencies and the damping ratios that through the comparison with the data of the initial conditions can de- tect the anomalies and then the intrinsic vulnerabilities. Through the curvature modal shape methods and the structural irregularity indices applied to different phases, it was possible evaluate the imperfection and the induced damage entity

Refined Rigid Block Model for In-Plane Loaded Masonry

In this work, a refined rigid block model is proposed for studying the in-plane behavior of regular masonry. The rigid block model is based on an existing discrete/rigid model with rigid blocks and elastoplastic interfaces that already proven its effectiveness in representing masonry behavior in linear and nonlinear fields. In this case, the proposed model is improved by assuming rigid quadrilateral elements connected by one-dimensional nonlinear interfaces, which are adopted both to represent mortar (or dry) joints between the blocks and also to represent inner potential cracks into the blocks. Furthermore, the softening behavior of interfaces in tension and shear is taken into account. Several numerical tests are performed by considering masonry panels with regular texture subjected to compression and shear. Particular attention is given to the collapse mechanisms and the pushover curves obtained numerically and compared with existing numerical and laboratory results. Furthermore, the numerical tests aim to evaluate the applicability limits of the proposed model with respect to existing results

Adaptation of DIC technique for simplified applications in experimental mechanics

The literature and practical application of Digital Image Correlation (DIC) present sophisticated methodologies and algorithms that through a correlation between image data, capture complex strains and deformation fields. However, its application requires extensive surface preparations, careful calibrations, high computational capabilities, and in some cases is still susceptible to errors. Through two experimental campaigns, this paper presents an adaptation of the 2D Digital Image Correlation (2D-DIC) technique, where instead of a speckle pattern to derive full-field deformation data, markers with high contrast features are adopted to extract point-wise strains. The primary goal of this adaptation is to define an approachable methodology for researchers without any background in DIC or image analysis and offer an additional tool set for experimental campaigns

DIC technique for experimental validation of higher order numerical models

This paper presents an adaptation to the Digital Image Correlation (DIC) technique to aid and improve standard measurement methods in experimental mechanics. The practical application is demonstrated by the validation of the Cosserat Continuum model, using small-scale masonry specimens. Numerical models, such as the Cosserat continuum, play an important role in the identification and description of the mechanical behaviour of structures. Especially when it comes to anisotropic and quasi-brittle materials like masonry, these models are needed to evaluate significant aspects like performance, safety, or the effects of various strengthening interventions. The experimental investigation to validate a numerical model is not always straightforward and several of them remain theoretical. Addressing this, the experimentation presented in this paper evaluates the Cosserat identification in shear, where along with simple shear deformation, rigid rotations, micro rotations and micro couples are also exhibited. With such complex deformations, conventional techniques, such as strain gauges, or extensometers can no longer be adopted. The adapted DIC allows the quantification of these deformation data and validates the numerical model

Refined Rigid Block Model for In-Plane Loaded Masonry

In this work, a refined rigid block model is proposed for studying the in-plane behavior of regular masonry. The rigid block model is based on an existing discrete/rigid model with rigid blocks and elastoplastic interfaces that already proven its effectiveness in representing masonry behavior in linear and nonlinear fields. In this case, the proposed model is improved by assuming rigid quadrilateral elements connected by one-dimensional nonlinear interfaces, which are adopted both to represent mortar (or dry) joints between the blocks and also to represent inner potential cracks into the blocks. Furthermore, the softening behavior of interfaces in tension and shear is taken into account. Several numerical tests are performed by considering masonry panels with regular texture subjected to compression and shear. Particular attention is given to the collapse mechanisms and the pushover curves obtained numerically and compared with existing numerical and laboratory results. Furthermore, the numerical tests aim to evaluate the applicability limits of the proposed model with respect to existing results

Visually Evoked Postural Responses (VEPRs) in Children with Vestibular Migraine

Vestibular migraine (VM) is the most common cause of episodic vertigo in children. Vertigo, nausea, dizziness and unsteadiness are often complained of by children with migraine, which can precede, follow or be present simultaneously with headache. The aim of this study was to use posturography to investigate the visually evoked postural responses (VEPRs) of children with VM and compare them to data obtained from children with primary headache (M) and controls (C). Twenty children diagnosed as affected by VM, nineteen children with M without aura and twenty healthy subjects were recruited in this cross-sectional study. Posturography was performed by a standardized stabilometric force-platform (Svep-Politecnica) in the following conditions: open eyes (OE), closed eyes (CE) and during full-field horizontal optokinetic stimulation (OKN-S). Electronystagmography was performed simultaneously to analyze optokinetic reflex parameters. In the OE condition, no difference was found between groups with respect to body sway area. In contrast, this parameter increased in the two pathological groups with respect to controls in the CE condition. The optokinetic stimulations also induced a similar increase of body sway area in the M group relative to controls, but a further increase was elicited in the VM group. Electronystagmographic recording also revealed different optokinetic reflex parameters in the latter groups. This study disclosed an abnormal sensitivity of children with M and VM to full-field moving scenes and a consequent destabilization of posture, as documented by the abnormal VEPRs. Children with VM were particularly exposed to this risk. Possible clinical implications of these findings are discusse