1,721,125 research outputs found
A simple mixed finite element model for composite beams with partial interaction
No full textA simple and effective mixed finite element model is proposed for studying the behavior of beams with composite section, with particular reference to two-layer beams with partial interaction, namely, steel–concrete, timber–concrete, and two-layer laminated glass beams. The model is based on a mixed variational formulation, which as independent fields assumes the displacements of each layer and the shear stresses transmitted by the connections between the layers. The effectiveness of the model, which automatically satisfies the Newmark kinematic hypothesis for a composite beam, is evaluated by performing a set of numerical tests and comparing results with existing analytical and numerical solutions; furthermore, the convergence of the model to the well-known layered and monolithic beam behavior is shown. Numerical tests are performed in the linear elastic field, but the possible model extensions to the field of material and geometric nonlinearity are highlighted,
together with a further refinement of the numerical model
Static and buckling analysis of thin beams on an elastic layer
No full textIn this work, a simple and effective numerical model for sandwich composites and/or thin films on an elastic layer is proposed. The Euler–Bernoulli beam hypothesis and an approximate expression of the Green's function of an elastic layer on a rigid base are adopted. The procedure is based on existing contributions, but the resulting power series expansion is more accurate and validated by means of a finite element model of the layer. A simple finite element–boundary integral equation approach is then adopted for performing static and buckling analysis of the Euler–Bernoulli beam in frictionless contact with the elastic layer. The proposed approach is based on a mixed variational formulation that assumes both beam displacements and contact reactions between the beam and the layer as independent fields. The influence of the layer height and rigid base contact type is taken into account, together with a parameter that considers the ratio between the beam and layer stiffness. Numerical tests show that a beam on a thick layer unbonded to the rigid base behaves similarly to a beam on a half-plane. On the other hand, a beam on a thin layer bonded to the rigid base is characterized by less deformability, large contact reactions at beam ends, and by different critical loads, with a low convergence speed to the behavior of a beam on a half-plane
A Mixed FEM for Studying Jointed Concrete Pavement Blowups
Full text linkThis work aims to study the compressive buckling and consequent blowup of jointed concrete pavements due to thermal rise. For this purpose, a simple and effective mixed FEM, originally introduced for performing static and buckling analyses of beams on elastic supports, is extended for performing a preliminary study of jointed concrete pavements. An elastic Euler–Bernoulli beam in frictionless and bilateral contact with an elastic support is considered. Three different elastic support models are assumed, namely a Winkler support, an elastic half-space (3D), and half-plane (2D). The transversal pavement joint or crack is modeled employing a hinge at the beam midpoint with nil rotational stiffness. Numerical tests are performed by determining critical loads and the corresponding modal shapes, with particular attention to the first minimum critical load related to pavement blowup. From a theoretical point of view, the results show that minimum critical loads converge to existing results in the case of Winkler support, whereas new results are obtained in the case of the 2D and 3D support types. Associated modal shapes have maximum upward displacements at the beam midpoint. The second and subsequent critical loads, together with the corresponding sinusoidal modal shapes, converge to existing results. From a practical point of view, minimum critical loads represent a lower bound for estimating axial forces due to thermal variation causing jointed pavement blowup
A simple mixed finite element model for laminated glass beams
No full textA simple and effective beam finite element model is here proposed for studying the behaviour of elastic laminated glass beams made of two external glass layers connected by a polymeric thin interlayer, able to transmit only shear stresses. The finite element model is based on a mixed variational formulation, which assumes as independent fields the horizontal and vertical translations and transverse section rotations of both glass layers, together with interlayer shear stresses. Several numerical tests are performed showing the effectiveness of the proposed model and its convergence to the well-known upper (monolithic) and lower (layered) limits for a laminated glass beam
DISCRETE AND CONTINUOUS MODELS FOR THE IN PLANE MODAL ANALYSIS OF MASONRY STRUCTURES
No full textA modal analysis, developed in plane dynamics and linear elasticity, for periodic masonry structure is presented and validated both by means of a continuum modelling within the frame of the micropolar continuum theory and of a discrete model (DEM) within the
frame of a molecular dynamic algorithm.
For running-bond masonry brickwork numerical micropolar models already exist [1,2] in
static frameworks [2] and in dynamic frameworks [3,4].
Here the aim is twofold: i) a multi-scale modal analysis both at Representative Elementary Volume (REV) level -micro-scale- and at masonry panel level -macro-scale-; ii) a multimodel analysis both with continuum micro-structured and discrete models such as to evaluate
sensitivity to masonry local microstructure and sensitivity to characteristic length of REV by reference to masonry panel size.
Two models are presented and compared. A discrete element model and a continuous micropolar model based on analytical homogenization procedures. Both models are based on the following assumptions: i) the structure is composed of rigid blocks; ii) the mortar joints are modelled as interfaces. The rigid block hypothesis is particularly suitable for historical masonry, in which stone blocks may be assumed as rigid bodies. Continuum homogenized
model provides, in an analytical form, constitutive equivalent elastic functions, mass and inertia; discrete model describes masonry as a rigid skeleton such as to evaluate both its global and local behaviour.
A parametric analysis is carried out to investigate the effect of i) masonry texture (running versus header bond); ii) size of heterogeneity (block dimensions) respect panel dimensions.
Modal analysis is hence carried on for a REV and different panels. Focus is on the sensitivity to heterogeneity size such as to verify models reliability and applicability field
Static stiffness of rigid foundation resting on elastic half-space using a Galerkin boundary element method
No full textIn this work, a simple and effective numerical model is proposed for studying flexible and rigid foundations in bilateral and frictionless contact with a three-dimensional elastic half-space. For this purpose, a Galerkin Boundary Element Method for the substrate is introduced, and both surface vertical displacements and half-space tractions are discretized by means of a piecewise constant function. The work focuses on a transversely isotropic substrate having the plane of isotropy parallel to the half-space boundary, hence the relationship between vertical displacements and half-space reactions is given by Michell solution, reducing to Boussinesq solution for an isotropic half-space. Several numerical tests are performed for showing the effectiveness of the model, on one hand by determining vertical displacements of flexible rectangular foundations subjected to vertical pressures, on the other hand by accurately determining the translational and rotational stiffness of rigid rectangular and L-shaped foundations. Particular attention is given to the determination of the center of stiffness in case of unsymmetrical foundations, since it turns out to be not coincident with foundation area centroid
Nonlinear analysis of structures on elastic half-space by a FE-BIE approach
No full textIn 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
DISCRETE ELEMENT MODEL FOR IN-PLANE LOADED VISCOELASTIC MASONRY
No full textA viscoelastic constitutive model is proposed to evaluate the evolution in time of historical masonry behavior. Masonry structures may be subject, over time, to damage due to creep phenomena, accompanied by a consequent redistribution of stresses and strains. Two models are presented and compared. A discrete element model and a continuous model based on analytical homogenization procedures. Both models are based on the following assumptions: (i) the structure is composed of rigid blocks; (ii) the time dependence of masonry behavior is concentrated in mortar joints, modelled as viscoelastic interfaces. The rigid block hypothesis is particularly suitable for historical masonry, in which stone blocks may be assumed as rigid bodies; the hypothesis of viscoelastic mortar is based on the observation that nonlinear phenomena may be concentrated in mortar joints. The continuum homogenized model provides, in an analytical form, constitutive equivalent viscous functions; the discrete model describes masonry as a rigid skeleton such as to evaluate both its global and local behavior. A parametric analysis is carried out to investigate the effect of (i) mortar-to-brick thickness ratio; (ii) masonry texture (running versus header bond); and (iii) size of heterogeneity (block dimensions) with respect to panel dimensions. Elementary cases are proposed to directly compare constitutive functions of continuum and discrete models. In addition, a meaningful case is proposed: a masonry panel in which the principal stresses are both of compression and the no-tension assumption may therefore be discounted. A further investigation pointed out the sensitivity to heterogeneity size such as to verify model reliability and applicability field
Discrete approaches for the nonlinear analysis of in plane loaded masonry walls : Molecular dynamic and static algorithm solutions
No full textThe aim of the paper is to present and validate a non commercial discrete element model (DEM) code for the nonlinear analysis of in plane loaded masonry panels, with dry or mortar joints. Such model is based on the hypothesis of rigid blocks and joints modeled as interfaces, that turn out to be both suitable for representing the behavior of ancient masonry, characterized by joint size negligible with respect to block size and block stiffness larger than joint stiffness. Hence, the elastic and inelastic behavior of a masonry assemblage is concentrated at joints by defining their stiffness and adopting a Mohr-Coulomb law as a restraint for interfacial actions. The proposed strategy is based on two approaches: a static solution method and a molecular dynamics algorithm. The static solution method allows to determine the stiffness matrix of a masonry panel and to update such matrix accounting for actual joint stiffness and blocks arrangement. Such method turns out to be computationally faster and equally effective with respect to the molecular dynamics one for performing incremental analysis of in plane loaded masonry panels. On the other hand, the molecular dynamics method is computationally less onerous than the static solution method, since it does not require to define and update panel stiffness matrix and to invert it for determining displacements. Both approaches are used and critically compared for solving several case studies of masonry panels modeled by DEM. In addition, it must be pointed out that results in terms of ultimate loads and collapse mechanisms are in good agreement with existing experimental data and numerical solutions
A full 3D rigid block model for the collapse behaviour of masonry walls
No full textThis paper presents and validates a non-commercial rigid block model code for performing pushover analysis of one leaf masonry assemblages with regular texture, in three dimensional field. Hypotheses of rigid blocks and joints modelled as interfaces are adopted for representing historic masonry behaviour, characterized by dry joints or weak mortar joints having negligible size with respect to block size. Masonry elastic and inelastic behaviour is concentrated at joints by defining their normal, shear, bending and torsion stiffness and strength, adopting a Mohr-Coulomb criterion for restraining interface actions. The proposed model is an extension to the field of material nonlinearity of an existing code, moreover nonlinear analyses follow an effective approach introduced by authors for the in-plane case, based on the determination and update of the stiffness matrix of the masonry assemblage during the incremental analysis, accounting for damage.
A numerical experimentation is performed for determining limit load multipliers and collapse mechanisms of several masonry walls subject to in-plane actions generated by self-weight and out-of-plane actions that may cause tilting or toppling of masonry assemblage portions. Dry and mortar joints are considered and existing case studies are adopted for calibrating the proposed model and evaluating its effectiveness
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