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Shear Deformation (shear + deformation)
Selected AbstractsInfluence of Semi-Rigid Connections and Local Joint Damage on Progressive Collapse of Steel FrameworksCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 3 2010Yuxin Liu This article extends the threat-independent method for progressive-failure analysis of rigid frames to analysis accounting for semi-rigid connections. The influence of joint damage caused by disengagement of member(s) is also considered in the analysis, and the degree of damage is modeled by a health index. A compound element model is employed to include the contributions of nonlinear behavior of beam-to-column connections, connection and member-end damage, member inelasticity, member shear deformation, and geometrical nonlinearity to structural response. Four beam collapse modes are illustrated for the progressive collapse analysis associated with debris loading generated when disengaged structural components fall onto lower parts of the structure. The impact effect is taken into account for the quasi-static nonlinear analysis by utilizing an impact amplification factor according to GSA and DoD guidelines. Any progressive collapse occurring thereafter involves a series of collapse events associated with topological changes of the frame. The analysis procedure is illustrated for the progressive collapse behavior of two planar steel frames. The results demonstrate that the proposed method is potentially an effective tool for the progressive collapse analysis of semi-rigid steel frames under abnormal loading events. [source] Physics-based GPS data inversion to estimate three-dimensional elastic and inelastic strain fieldsGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2010Akemi Noda SUMMARY The Earth's crust is macroscopically treated as a linear elastic body, but it includes a number of defects. The occurrence of inelastic deformation such as brittle fracture at the defects brings about elastic deformation in the surrounding regions. The crustal deformation observed through geodetic measurements is the sum of the inelastic deformation as source and the elastic deformation as effect. On such a basic idea, we created a theory of physics-based strain analysis with general source representation by moment tensor, and developed an inversion method to separately estimate 3-D elastic and inelastic strain fields from GPS data. In this method, first, the optimum distribution of moment density tensor is determined from observed GPS data by using Akaike's information criterion. Then, the elastic and inelastic strain fields are obtained from the optimum moment tensor distribution by theoretical computation and direct conversion with elastic compliance tensor, respectively. We applied the inversion method to GPS horizontal velocity data, and succeeded in separately estimating 3-D elastic and inelastic strain rate fields in the Niigata,Kobe transformation zone, central Japan. As for the surface patterns of total strain, the present results of 3-D physics-based inversion analysis accord with the previous results of 2-D geometric inversion analysis. From the 3-D patterns of the inverted elastic and inelastic strain fields, we revealed that the remarkable horizontal contraction in the Niigata,Kobe transformation zone is elastic and restricted near the surface, but the remarkable shear deformation is inelastic and extends over the upper crust. [source] Plastic Dissipation Mechanisms in Periodic Microframe-Structured PolymersADVANCED FUNCTIONAL MATERIALS, Issue 9 2009Lifeng Wang Abstract Novel lightweight micro- and nanostructured materials are being used as constituents in hierarchically structured composites for providing high stiffness, high strength, and energy absorbing capability at low weight. Three dimensional SU-8 periodic microframe materials with submicrometer elements exhibit unusual large plastic deformations. Here, the plastic dissipation and mechanical response of polymeric microframe structures is investigated using micromechanical modeling of large deformations. Finite element analysis shows that multiple deformation domains initiate, stabilize, and then spread plasticity through the structure; simulated deformation mechanisms and deformation progression are found to be in excellent agreement with experimental observation. Furthermore, the geometry can be used to tailor aspects of 3D behavior such as effective lateral contraction ratios (elastic and plastic) during tensile loading as well as negative normal stress during simple shear deformation. The effects of structural geometry on mechanical response are also studied to tailor and optimize mechanical performance at a given density. These quantitative investigations enable simulation-based design of optimal lightweight material microstructures for dissipating energy. [source] Uniform asymptotic Green's functions for efficient modeling of cracks in elastic layers with relative shear deformation controlled by linear springsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 3 2009Anthony P. Peirce Abstract We present a uniform asymptotic solution (UAS) for a displacement discontinuity (DD) that lies within the middle layer of a three-layer elastic medium in which relative shear deformation between parallel interfaces is controlled by linear springs. The DD is assumed to be normal to the two interfaces between the elastic media. Using the Fourier transform method we construct a leading term in the asymptotic expansion for the spectral coefficient functions for a DD in a three-layer-spring medium. Although a closed-form solution will require a solution in terms of an infinite series, we demonstrate how this UAS can be used to construct highly efficient and accurate solutions even in the case in which the DD actually touches the interface. We compare the results using the Green's function UAS solution for a crack crossing a soft interface with results obtained using a multi-layer boundary element method. We also present results from an implementation of the UAS Green's function approach in a pseudo-3D hydraulic fracturing simulator to analyze the effect of interface shear deformation on the fracture propagation process. These results are compared with field measurements. Copyright © 2008 John Wiley & Sons, Ltd. [source] Non-isothermal plasticity model for cyclic behaviour of soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2008L. Laloui Abstract On the one hand, it has been observed that liquefaction-induced shear deformation of soils accumulates in a cycle-by-cycle pattern. On the other hand, it is known that heating could induce plastic hardening. This study deals with the constitutive modelling of the effect that heat may have on the cyclic mechanical properties of cohesive soils, a relatively new area of interest in soil mechanics. In this paper, after a presentation of the thermo-mechanical framework, a non-isothermal plasticity cyclic model formulation is presented and discussed. The model calibration is described based on data from laboratory sample tests. It includes numerical simulations of triaxial shear tests at various constant temperatures. Then, the model predictions are compared with experimental results and discussed in the final section. Both drained and undrained loading conditions are considered. The proposed constitutive model shows good ability to capture the characteristic features of behaviour. Copyright © 2007 John Wiley & Sons, Ltd. [source] Finite element modelling of thick plates on two-parameter elastic foundationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 14 2001Ryszard Buczkowski Abstract This paper is intended to give some information about how to build a model necessary for bending analysis of rectangular and circular plates resting on a two-parameter elastic foundation, subjected to combined loading and permitting various types of boundary conditions. The formulation of the problem takes into account the shear deformation of the plate and the surrounding interaction effect outside the plate. The numerical model based on an 18-node zero-thickness isoparametric interface element interacting with a thick Reissner,Mindlin plate element with three degrees of freedom at each of the nine nodes, which enforce C0 continuity requirements for the displacements and rotations of the midsurface, is proposed. Stiffness matrices of a special interface element are superimposed on the global stiffness matrix to represent the stiffening elastic foundation under and beyond the plate. Some numerical examples are given to illustrate the advantages of the method presented. Copyright © 2001 John Wiley & Sons, Ltd. [source] DQEM analysis of out-of-plane deflection of non-prismatic curved beam structures considering the effect of shear deformationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 7 2008Chang-New Chen Abstract The development of differential quadrature element method (DQEM) out-of-plane deflection analysis model of curved non-prismatic beam structures considering the effect of shear deformation was carried out. The DQEM uses the differential quadrature (DQ) to discretize the governing differential equation defined on each element, the transition conditions defined on the inter-element boundary of two adjacent elements and the boundary conditions of the beam. Numerical results solved by the developed numerical algorithm are presented. The convergence of the developed DQEM analysis model is efficient. Copyright © 2006 John Wiley & Sons, Ltd. [source] Efficient mixed Timoshenko,Mindlin shell elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2002G. M. Kulikov Abstract The precise representation of rigid body motions in the displacement patterns of curved Timoshenko,Mindlin (TM) shell elements is considered. This consideration requires the development of the strain,displacement relationships of the TM shell theory with regard to their consistency with the rigid body motions. For this purpose a refined TM theory of multilayered anisotropic shells is elaborated. The effects of transverse shear deformation and bending-extension coupling are included. The fundamental unknowns consist of five displacements and eight strains of the face surfaces of the shell, and eight stress resultants. On the basis of this theory the simple and efficient mixed models are developed. The elemental arrays are derived using the Hu,Washizu mixed variational principle. Numerical results are presented to demonstrate the high accuracy and effectiveness of the developed 4-node shell elements and to compare their performance with other finite elements reported in the literature. Copyright © 2002 John Wiley & Sons, Ltd. [source] A new shear flexible cubic spline plate element for vibration analysisINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002B. P. Patel Abstract Here, a new cubic B-spline plate element is developed using field consistency principle, for vibration analysis. The formulation includes anisotropy, transverse shear deformation, in-plane and rotary inertia effects. The element is based on a laminated refined plate theory, which satisfies the interface transverse shear stress and displacement continuity, and has a vanishing shear stress on the top and bottom surfaces of the plates. The lack of consistency in the shear strain field interpolations in its constrained physical limits produces poor convergence and results in unacceptable solutions due to locking phenomenon. Hence, numerical experimentation for the evaluation of natural frequencies of plates is carried out to check this deficiency with a series of assumed shear strain functions, redistributed in a field consistent manner. Copyright © 2002 John Wiley & Sons, Ltd. [source] Nucleation and growth of myrmekite during ductile shear deformation in metagranitesJOURNAL OF METAMORPHIC GEOLOGY, Issue 7 2006L. MENEGON Abstract Myrmekite is extensively developed along strain gradients of continuous, lower amphibolite facies shear zones in metagranites of the Gran Paradiso unit (Western Alps). To evaluate the role of stress, strain energy and fluid phase in the formation of myrmekite, we studied a sample suite consisting of weakly deformed porphyric granites (WDGs), foliated granites (FGs) representative of intermediate strains, and mylonitic granites (MGs). In the protolith, most K-feldspar is microcline with different sets of perthite lamellae and fractures. In the WDGs, abundant quartz-oligoclase myrmekite developed inside K-feldspar only along preexisting perthite lamellae and fractures oriented at a high angle to the incremental shortening direction. In the WDGs, stress played a direct role in the nucleation of myrmekites along interfaces already characterized by high stored elastic strain because of lattice mismatch between K-feldspar and albite. In the FGs and MGs, K-feldspar was progressively dismembered along the growing network of microshear zones exploiting the fine-grained recrystallized myrmekite and perthite aggregates. This was accompanied by a more pervasive fluid influx into the reaction surfaces, and myrmekite occurs more or less pervasively along all the differently oriented internal perthites and fractures independently of the kinematic framework of the shear zone. In the MGs, myrmekite forms complete rims along the outer boundary of the small K-feldspar porphyroclasts, which are almost completely free of internal reaction interfaces. Therefore, we infer that the role of fluid in the nucleation of myrmekite became increasingly important as deformation progressed and outweighed that of stress. Mass balance calculations indicate that, in Al,Si-conservative conditions, myrmekite growth was associated with a volume loss of 8.5%. This resulted in microporosity within myrmekite that enhanced the diffusion of chemical components to the reaction sites and hence the further development of myrmekite. [source] P,T conditions of decompression of the Limpopo high-grade terrane: record from shear zonesJOURNAL OF METAMORPHIC GEOLOGY, Issue 3 2001C. A. Smit Abstract The Southern Marginal Zone of the late Archean Limpopo Belt of southern Africa is an example of a high-grade gneiss terrane in which both upper and lower crustal deformational processes can be studied. This marginal zone consists of large thrust sheets of complexly folded low-strain gneisses, bound by an imbricate system of kilometre-wide deep crustal shear zones characterized by the presence of high-strain gneisses (,primary straight gneisses'). These shear zones developed during the decompression stage of this high-grade terrane. Low- and high-strain gneisses both contain similar reaction textures that formed under different kinematic conditions during decompression. Evidence for the early M1/D1 metamorphic phase (> 2690 Ma) is rarely preserved in low-strain gneisses as a uniform orientation of relict Al-rich orthopyroxene in the matrix and quartz and plagioclase inclusions in the cores of early (M1) Mg-rich garnet porphyroblasts. This rare fabric formed at >,820 °C and >,7.5 kbar. The retrograde M2/D2 metamorphic fabric (2630,2670 Ma) is well developed in high-strain gneisses from deep crustal shear zones and is microscopically recognized by the presence of reaction textures that formed synkinematically during shear deformation: M2 sigmoid-shaped reaction textures with oriented cordierite,orthopyroxene symplectites formed after the early M1 Mg-rich garnet porphyroblasts, and syn-decompression M2 pencil-shaped garnet with oriented inclusions of sillimanite and quartz formed after cordierite under conditions of near-isobaric cooling at 750,630 °C and 6,5 kbar. The symplectites and pencil-shaped garnet are oriented parallel to the shear fabric and in the stretching direction. Low-strain gneisses from thrust sheets show similar M2 decompression cooling and near-isobaric cooling reaction textures that formed within the same P,T range, but under low-strain conditions, as shown by their pseudo-idioblastic shapes that reflect the contours of completely replaced M1 garnet and randomly oriented cordierite,orthopyroxene symplectites. The presence of similar reaction textures reflecting low-strain conditions in gneisses from thrust sheets and high-strain conditions in primary straight gneisses suggests that most of the strain during decompression was partitioned into the bounding shear zones. A younger M3/D3 mylonitic fabric (< 2637 Ma) in unhydrated mylonites is characterized by brittle deformation of garnet porphyroclasts and ductile deformation of the quartz,plagioclase,biotite matrix developed at <,600 °C, as the result of post-decompression shearing under epidote,amphibolite facies conditions. [source] Biomechanics of the rostrum and the role of facial suturesJOURNAL OF MORPHOLOGY, Issue 1 2003Katherine L. Rafferty Abstract The rostrum is a large diameter, thin-walled tubular structure that receives loads from the teeth. The rostrum can be conceptualized both as a rigid structure and as an assemblage of several bones that interface at sutures. Using miniature pigs, we measured in vivo strains in rostral bones and sutures to gain a better understanding of how the rostrum behaves biomechanically. Strains in the premaxillary and nasal bones were low but the adjacent maxillary-premaxillary, internasal, and intermaxillary suture strains were larger by an order of magnitude. While this finding emphasizes the composite nature of the rostrum, we also found evidence in the maxillary and nasal bones for rigid structural behavior. Namely, maxillary strain is consistent with a short beam model under shear deformation from molar loading. Strain in the nasal bones is only partially supported by a long beam model; rather, a complex pattern of dorsal bending of the rostrum from incisor contact and lateral compression is suggested. Torsion of the maxilla is ruled out due to the bilateral occlusion of pigs and the similar working and balancing side strains, although it may be important in mammals with a unilateral bite. Torsional loading does appear important in the premaxillae, which demonstrate working and balancing side changes in strain orientation. These differences are attributed to asymmetrical incisor contact occurring at the end of the power stroke. J. Morphol. 257:33,44, 2003. © 2003 Wiley-Liss, Inc. [source] Measuring anisotropic thermal conduction in polyisobutylene following step shear strainsAICHE JOURNAL, Issue 3 2000Hadjira Iddir The connection between polymer chain orientation and several macroscopic properties in a polymer melt was studied using mechanical and optical techniques. Anisotropic thermal conductivity following shear deformation was measured using forced Rayleigh light scattering, the refractive index tensor is followed using birefringence measurements, and the stress was measured mechanically in a parallel-plate rheometer. The thermal diffusivity measured in the flow and neutral directions increased and decreased, respectively, immediately following the deformation. These quantities then relaxed to the equilibrium value on the time-scale of the stress-relaxation memory. Comparison of the difference between measured flow and neutral direction thermal diffusivities with the analogous flow-induced birefringence in the same deformation provided indirect evidence for a linear relation between stress and thermal diffusivity at two different values of strain. Mechanical measurements were used to characterize the memory of the fluid. [source] Rheological Investigations in Understanding Shear-Enhanced Crystallization of Isotactic Poly(propylene)/Multi-Walled Carbon Nanotube CompositesMACROMOLECULAR RAPID COMMUNICATIONS, Issue 11 2007Ke Wang Abstract A novel experimental technique to follow the crystallization processes of poly(propylene)/MWCNT composites that experience a steady shear deformation using dynamic melt rheometry is described. The effects of heterogeneous nucleation, temperature, and preshear on the crystallization behaviors were determined. A quantitative evaluation of crystallization kinetics difference between quiescent and preshear conditions could be achieved. By combining rheology with POM, we demonstrate that two different crystallization processes account for the shear-enhanced crystallization at low and high temperatures, respectively. [source] Anomalies, influencing factors, and guidelines for DMA testing of fiber reinforced compositesPOLYMER COMPOSITES, Issue 7 2009Gowthaman Swaminathan This study systematically assessed the measurement of dynamic properties of a range of fiber reinforced composite materials using dynamic mechanical analysis (DMA) instrument. The discrepancy in the moduli from DMA to ASTM tests was investigated. The study showed that proper specimen preparation, maintaining appropriate aspect ratio (span to thickness ratio) to reduce the transverse shear deformation, and sufficient loading are critical to measure correct properties from DMA test. The guidelines on aspect ratio and loading for plastics to high-modulus carbon fiber composites are presented as a design chart and equations, respectively. The study also found that the glass transition temperature (Tg) was independent of specimen aspect ratio and Tg is lower for multidirectional composites when compared with its unidirectional composites. The particle interleaved T800H/3900-2 composite showed two glass transition temperatures (140 and 198°C), the lower value is due to the effect of interleaving by thermoplastic particles, and the higher value is the Tg of its base matrix. This lowering of Tg would have significant effect on the application temperature of the material. This phenomenon was not observed here to fore in the literature. POLYM. COMPOS., 2009. © 2009 Society of Plastics Engineers [source] Fracture behavior of styrene-ethylene-propylene rubber-toughened polypropylenePOLYMER ENGINEERING & SCIENCE, Issue 9 2000G.-X. Wei The morphology and fracture behavior of isotactic polypropylene toughened by styrene-ethylene-propylene (PP/SEP) were investigated. The SEP rubber, having an average particle size of 0.2 µm, is found to be well dispersed in the PP matrix. The fracture toughness of SEP-modified PP is greatly improved. The toughening mechanism investigation shows that a widespread crazing zone is generated in the crack tip damage zone. An intense narrow damage band in the center of crazed zone is formed. Crazing and shear yielding are found to be the dominant toughening mechanisms in PP/SEP. The crazes are initiated only by large SEP particles in the blend. The small SEP particles (< 0.3 µm) can neither cavitate nor trigger crazing. As a result, large scale shear deformation is suppressed in this blend. These findings are consistent with the notion that the crack tip plane strain constraint has to be relieved in magnitude in order for the deviatoric stress to reach a critical value for widespread shear banding. [source] Viscoelasticity of Hyaluronan and Nonhyaluronan Based Vocal Fold Injectables: Implications for Mucosal Versus Muscle Use,THE LARYNGOSCOPE, Issue 3 2007Trace Caton BS Abstract Objectives: The purpose of this study was to measure and compare biomechanical properties of commonly used vocal fold injectates Cymetra, Radiesse, Restylane, Hylaform, and one investigational injectate, Carbylan-GSX 5%, to determine suitability for mucosal injection. Study Design: Rheologic investigation. Methods: Oscillatory shear stress was applied to five samples of each injectate using a parallel plate controlled stress rheometer. Shear stress, shear strain, and strain rate associated with the oscillatory shear deformation were computed from the prescribed torque and measured angular velocity; viscoelastic data were obtained on the basis of these functions. Values calculated included elastic shear moduli, viscous moduli, and dynamic viscosity as a function of oscillatory frequency (0.01,150 Hz). Results: Elastic moduli for all samples increased as the frequency increased. Hyaluronan based materials were all comparable with each other and at least an order of magnitude lower than the stiffer and more viscous Cymetra and Radiesse. Carbylan-GSX 5% was found to have almost identical values to Hylaform with the exception of its mean viscosity, which was noticeably lower. Conclusions: Hyaluronan based biomaterials offer less resistance to flow and stiffness and may be better suited for injections into the mucosa, whereas Cymetra and Radiesse appear to be appropriate for injections into muscle. Viscoelastic properties of Hylaform and Carbylan-GSX 5% were found to most resemble that of the human vocal fold mucosa. [source] Biomechanics of cartilage articulation: Effects of lubrication and degeneration on shear deformationARTHRITIS & RHEUMATISM, Issue 7 2008Benjamin L. Wong Objective To characterize cartilage shear strain during articulation, and the effects of lubrication and degeneration. Methods Human osteochondral cores from lateral femoral condyles, characterized as normal or mildly degenerated based on surface structure, were selected. Under video microscopy, pairs of osteochondral blocks from each core were apposed, compressed 15%, and subjected to relative lateral motion with synovial fluid (SF) or phosphate buffered saline (PBS) as lubricant. When cartilage surfaces began to slide steadily, shear strain (Exz) and modulus (G) overall in the full tissue thickness and also as a function of depth from the surface were determined. Results In normal tissue with SF as lubricant, Exz was highest (0.056) near the articular surface and diminished monotonically with depth, with an overall average Exz of 0.028. In degenerated cartilage with SF as lubricant, Exz near the surface (0.28) was 5-fold that of normal cartilage and localized there, with an overall Exz of 0.041. With PBS as lubricant, Exz values near the articular surface were ,50% higher than those observed with SF, and overall Exz was 0.045 and 0.062 in normal and degenerated tissue, respectively. Near the articular surface, G was lower with degeneration (0.06 MPa, versus 0.18 MPa in normal cartilage). In both normal and degenerated cartilage, G increased with tissue depth to 3,4 MPa, with an overall G of 0.26,0.32 MPa. Conclusion During articulation, peak cartilage shear is highest near the articular surface and decreases markedly with depth. With degeneration and diminished lubrication, the markedly increased cartilage shear near the articular surface may contribute to progressive cartilage deterioration and osteoarthritis. [source] Initial stiffness of reinforced concrete structural walls with irregular openingsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 4 2010Bing Li Abstract Reinforced concrete (RC) structural walls with openings are the primary lateral-load-carrying elements utilized in many structures designed to resist earthquakes. A review of the technical literature shows that there is a considerable amount of uncertainty with regards to the elastic stiffness of these structures when subjected to seismic excitations. Current design practices often employ a stiffness reduction factor to deal with this uncertainty. In an attempt to develop additional information regarding the stiffness of these structures, this paper discusses an approach to determine the initial stiffness of RC structural walls with irregular openings and low aspect ratios. This approach would consider the effect of both flexural and shear deformations. As a part of this study, an analytical approach to determine stiffness was also developed and validated by comparing theoretical and experimental results obtained from six RC shear walls with irregular openings. Simple equations for assessing initial stiffness of RC structural walls with irregular openings are then proposed, based on these parametric case studies. Copyright © 2009 John Wiley & Sons, Ltd. [source] A mechanical model for elastomeric seismic isolation bearings including the influence of axial loadEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2009Sachie Yamamoto Abstract For the purpose of predicting the large-displacement response of seismically isolated buildings, an analytical model for elastomeric isolation bearings is proposed. The model comprises shear and axial springs and a series of axial springs at the top and bottom boundaries. The properties of elastomeric bearings vary with the imposed vertical load. At large shear deformations, elastomeric bearings exhibit stiffening behavior under low axial stress and buckling under high axial stress. These properties depend on the interaction between the shear and axial forces. The proposed model includes interaction between shear and axial forces, nonlinear hysteresis, and dependence on axial stress. To confirm the validity of the model, analyses are performed for actual static loading tests of lead,rubber isolation bearings. The results of analyses using the new model show very good agreement with the experimental results. Seismic response analyses with the new model are also conducted to demonstrate the behavior of isolated buildings under severe earthquake excitations. The results obtained from the analyses with the new model differ in some cases from those given by existing models. Copyright © 2008 John Wiley & Sons, Ltd. [source] Evaluation of pounding countermeasures and serviceability of elevated bridges during seismic excitation using 3D modelingEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 5 2004Ping Zhu Abstract This paper conducts elaborate analyses to evaluate the effectiveness of pounding countermeasures and the serviceability of elevated bridges subject to severe ground motions using detailed 3-dimensional non-linear modeling of an entire bridge structure system. A three-span elevated steel bridge is selected for a case study. The peak and residual magnitude of gaps between girders and the maximum shear deformations of bearings are computed and used in the serviceability evaluation. The results show that under proper configurations the mitigation devices work effectively in reducing pounding actions in both the longitudinal and rotational directions. Copyright © 2004 John Wiley & Sons, Ltd. [source] A geometrically and materially non-linear piezoelectric three-dimensional-beam finite element formulation including warping effectsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2008A. Butz Abstract This paper is concerned with a three-dimensional piezoelectric beam formulation and its finite element implementation. The developed model considers geometrically and materially non-linear effects. An eccentric beam formulation is derived based on the Timoshenko kinematics. The kinematic assumptions are extended by three additional warping functions of the cross section. These functions follow from torsion and piezoelectrically induced shear deformations. The presented beam formulation incorporates large displacements and finite rotations and allows the investigation of stability problems. The finite element model has two nodes with nine mechanical and five electrical degrees of freedom. It provides an accurate approximation of the electric potential, which is assumed to be linear in the direction of the beam axis and quadratic within the cross section. The mechanical degrees of freedom are three displacements, three rotations and three scaling factors for the warping functions. The latter are computed in a preprocess by solving a two-dimensional in-plane equilibrium condition with the finite element method. The gained warping patterns are considered within the integration through the cross section of the beam formulation. With respect to material non-linearities, which arise in ferroelectric materials, the scalar Preisach model is embedded in the formulation. This model is a mathematical model for the general description of hysteresis phenomena. Its application to piezoelectric materials leads to a phenomenological model for ferroelectric hysteresis effects. Here, the polarization direction is assumed to be constant, which leads to unidirectional constitutive equations. Some examples demonstrate the capability of the proposed model. Copyright © 2008 John Wiley & Sons, Ltd. [source] Locking-free finite elements for shear deformable orthotropic thin-walled beamsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2007F. Minghini Abstract Numerical models for finite element analyses of assemblages of thin-walled open-section profiles are presented. The assumed kinematical model is based on Timoshenko,Reissner theory so as to take shear strain effects of non-uniform bending and torsion into account. Hence, strain elastic-energy coupling terms arise between bending in the two principal planes and between bending and torsion. The adopted model holds for both isotropic and orthotropic beams. Several displacement interpolation fields are compared with the available numerical examples. In particular, some shape functions are obtained from ,modified' Hermitian polynomials that produce a locking-free Timoshenko beam element. Analogously, numerical interpolation for torsional rotation and cross-section warping are proposed resorting to one Hermitian and six Lagrangian formulation. Analyses of beams with mono-symmetric and non-symmetric cross-sections are performed to verify convergence rate and accuracy of the proposed formulations, especially in the presence of coupling terms due to shear deformations, pointing out the decay length of end effects. Profiles made of both isotropic and fibre-reinforced plastic materials are considered. The presented beam models are compared with results given by plate-shell models. Copyright © 2007 John Wiley & Sons, Ltd. [source] An exact sinusoidal beam finite elementPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Zdzislaw Pawlak The purpose of the paper is to derive an efficient sinusoidal thick beam finite element for the static analysis of 2D structures. A two,node, 6,DOF curved, sine,shape element of a constant cross,section is considered. Effects of flexural, axial and shear deformations are taken into account. Contrary to commonly used curvilinear co,ordinates, a rectangular co,ordinates system is used in the present analysis. First, an auxiliary problem is solved: a symmetric clamped,clamped sinusoidal arch subjected to unit nodal displacements of both supports is considered using the flexibility method. The exact stiffness matrix for the shear,flexible and compressible element is derived. Introduction of two parameters "n" and "t" enables the identification of shear and membrane influences in the element stiffness matrix. Basing on the principle of virtual work a full set of 18 shape functions related to unit support displacements is derived (total rotations of cross,sections, tangential and normal displacements along the element). The functions are found analytically in the closed form. They are functions of one linear dimensionless coordinate of x,axis and depend on one geometrical parameter of sinusoidal arch, height/span ratio "c" and on physical and geometrical properties of the element cross,section. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] | ||||||||||||||||||||||