Analysis of stiffened plates by the boundary element method

In this paper, a formulation for representation of stiffeners in plane stress by the boundary elements method (BEM) in linear analysis is presented. The strategy is to adopt approximations for the displacements in the central line of the stiffener. With this simplification the Spurious oscillations in the stress along stiffeners with small thickness is prevented. Worked examples are analyzed to show the efficiency of these techniques, especially in the insertion of very narrow sub-regions, in which quasi-singular integrals are calculated, with stiffeners that are much stiffer than the main domain. The results obtained with this formulation are very close to those obtained with other formulations. (C) 2007 Elsevier Ltd. All rights reserved.

Analysis of the Coupled Stretching-Bending Problem of Stiffened Plates by a BEM Formulation Based on Reissner's Hypothesis

In this work, the plate bending formulation of the boundary element method - BEM, based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by beams taking into account the membrane effects. The formulation is derived by assuming a zoned body where each sub-region defines a beam or a slab and all of them are represented by a chosen reference surface. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to reduce the number of degrees of freedom, the problem values defined on the interfaces are written in terms of their values on the beam axis. Initially are derived separated equations for the bending and stretching problems, but in the final system of equations the two problems are coupled and can not be treated separately. Finally are presented some numerical examples whose analytical results are known to show the accuracy of the proposed model.

An extended BEM formulation for plates reinforced by rectangular beams

This article presents a BEM formulation developed particularly for analysis of plates reinforced by rectangular beams. This is an extended version of a Previous paper that only took into account bending effects. The problem is now re-formulated to consider bending and membrane force effects. The effects of the reinforcements are taken into account by using a simplified scheme that requires application of ail initial stress field to locally correct the bending and stretching stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. To reduce the number of degrees of freedom related to the presence of the reinforcement, the proposed model was simplified to consider only bending and stretching rigidities in the direction of the beams. The complete model can be recovered by applying all six internal force correctors, corresponding to six degrees of freedom per node. Examples are presented to confirm the accuracy of the formulation and to illustrate the level of simplification introduced by this strong reduction in the number of degrees of freedom. (C) 2008 Elsevier Ltd. All rights reserved.

BEM formulation for reinforced plates

This article presents a BEM formulation developed to analyse reinforced plate bending. The reinforcements are formulated using a simplified scheme based on applying an initial moment field adopted to locally correct the stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. The increase in system stiffness due to the reinforcements can be taken into account independently for each coefficient. Thus, one can conveniently reduce the number of degrees of freedom required in considering the reinforcement. Only one degree-of-freedom is required at each internal node when taking into account only the flexural stiffness of beams. Examples are presented to confirm the accuracy of the formulation. (C) 2009 Elsevier Ltd. All rights reserved.

Strength Predictions of Hat Stiffened Plate

Hat Stiffened Plates are used in composite ships and are gaining popularity in metallic ship construction due to its high strength-to-weight ratio. Light weight structures will result in greater payload, higher speeds, reduced fuel consumption and environmental emissions. Numerical Investigations have been carried out using the commercial Finite Element software ANSYS 12 to substantiate the high strength-to-weight ratio of Hat Stiffened Plates over other open section stiffeners which are commonly used in ship building. Analysis of stiffened plate has always been a matter of concern for the structural engineers since it has been rather difficult to quantify the actual load sharing between stiffeners and plating. Finite Element Method has been accepted as an efficient tool for the analysis of stiffened plated structure. Best results using the Finite Element Method for the analysis of thin plated structures are obtained when both the stiffeners and the plate are modeled using thin plate elements having six degrees of freedom per node. However, one serious problem encountered with this design and analysis process is that the generation of the finite element models for a complex configuration is time consuming and laborious. In order to overcome these difficulties two different methods viz., Orthotropic Plate Model and Superelement for Hat Stiffened Plate have been suggested in the present work. In the Orthotropic Plate Model geometric orthotropy is converted to material orthotropy i.e., the stiffeners are smeared and they vanish from the field of analysis and the structure can be analysed using any commercial Finite Element software which has orthotropic elements in its element library. The Orthotropic Plate Model developed has predicted deflection, stress and linear buckling load with sufficiently good accuracy in the case of all four edges simply supported boundary condition. Whereas, in the case of two edges fixed and other two edges simply supported boundary condition even though the stress has been predicted with good accuracy there has been large variation in the deflection predicted. This variation in the deflection predicted is because, for the Orthotropic Plate Model the rigidity is uniform throughout the plate whereas in the actual Hat Stiffened Plate the rigidity along the line of attachment of the stiffeners to the plate is large as compared to the unsupported portion of the plate. The Superelement technique is a method of treating a portion of the structure as if it were a single element even though it is made up of many individual elements. The Superelement has predicted the deflection and in-plane stress of Hat Stiffened Plate with sufficiently good accuracy for different boundary conditions. Formulation of Superelement for composite Hat Stiffened Plate has also been presented in the thesis. The capability of Orthotropic Plate Model and Superelement to handle typical boundary conditions and characteristic loads in a ship structure has been demonstrated through numerical investigations.

A BEM formulation based on Reissner's theory to perform simple bending analysis of plates reinforced by rectangular beams

In this work, the plate bending formulation of the boundary element method (BEM), based on the Reissner's hypothesis, is extended to the analysis of plates reinforced by rectangular beams. This composed structure is modelled by a zoned plate, being the beams represented by narrow sub-regions with larger thickness. The integral equations are derived by applying the weighted residual method to each sub-region, and summing them to get the equation for the whole plate. Equilibrium and compatibility conditions are automatically imposed by the integral equations, which treat this composed structure as a single body. In order to decrease the number of degrees of freedom, some approximations are considered for both displacements and tractions along the beam width. The accuracy of the proposed model is illustrated by simple examples whose exact solution are known as well as by more complex examples whose numerical results are compared with a well-known finite element code.

Beitrag zur Entwicklung der Querschnittsgestaltung im Verbundbrückenbau

Die grafische Darstellung des Verbundquerschnittes mit einer oberen Betonplatte und einem darunter liegenden Stahlträger war seit seiner Vorstellung in den 1950er Jahren ein Symbol, das weit über die Theorie hinausging und weite Verbreitung in der Praxis des Verbundbrückenbaus fand. Seit den 1970er bzw. 1980er Jahren hat dieses Bild – bedingt durch neue und freiere Formen, Beton und Stahl miteinander zu kombinieren – seine Symbolhaftigkeit verloren. In Deutschland und Spanien wurde der Doppelverbund mit unten liegenden Betonplatten in Bereichen mit negativen Momenten eingeführt, in Frankreich werden Stahlträger auch in vorgespannten Betonquerschnitten eingebettet. Beide Ansätze haben dazu beigetragen, dass in der Gegenwart die Materialien Stahl und Beton im Verbundbau frei miteinander kombiniert werden können. On the development of sections in composite bridges. A comprehensive theory of composite construction was established in Germany by Sattler in 1953. The theoretical image of the composite section with a superior concrete slab and a lower metallic structure was shaped in addition to the analytical resolution. Theory and graphical representation were going to be known together in Europe. This figure was repeated in all theoretical and academic publications, so becoming an authentic icon of the composite section. Its translation to the bridge deck in flexion was obvious: the superior slab defines the tread platform, while the metallic structure was left off-hook at the bottom. Nevertheless, in continuous decks the section is not optimal at all in zones of negative bending moments. But the overcoming of the graphical representation of the theory did not happen immediately. It was produced after a process in which several European countries played an active role and where different mechanisms of technological transference were developed. One approach to this overcoming is the “double composite action”, with a lower concrete slab in areas of a negative bending moment. The first accomplishments, a bridge in Orasje built in 1968 with 134 m span, as well as the publications of the system proposed by Fabrizio de Miranda in 1971 did not extend nor had continuity. Spanish bridges by Fernández Ordoñez and Martínez Calzón used double composite action for the first time in 1979. The German team of Leonhard, Andrä und partners, has used it since the end of the 1980's to solve bridges of great span. Once the technology has been well known thanks to the ASCE International Congress and the Spanish International Meetings organised by the “Colegio de Ingenieros de Caminos”, double composite action has been integrated well into the structural vocabulary everywhere. In France the approach was different. What Michel Virlogeux calls “double floor composite section” was reached as an evolution of prestressed concrete bridges. In an experimental process widely known, the external prestressing allows weight reduction by diminishing the thickness of the concrete webs. The following step, in the 1980's, was the substitution of the webs by metallic elements: stiffened plates, trusses or folded plates. A direct result of this development is the Brass de la Plaine Bridge in the Reunion Island in 2001 with 280 m span. Both approaches have contributed to a freedom of design in composite construction in steel and concrete today.

Analysis of clamped square plates containing openings with stiffened edges /

Mode of access: Internet.

Vibrations of ring-stiffened cylindrical shells.

"AFSWP no. 873. Office of Naval Research. Contract no. Nonr-266 (08) Technical report no. 13. CU-13-55-ONR-266 (08)-CE."

Approximate determination of the frequencies of ring stiffened cylindrical shells.

"AFSWP no. 874. Office of Naval Research. Contract no. Nonr 266 (08) Technical report no. 14. CU-14-55-ONR-266 (08)-CE."

Chemical And Structural Analyses Of Titanium Plates Retrieved From Patients.

The aim of this study was to evaluate the microscopic structure and chemical composition of titanium bone plates and screws retrieved from patients with a clinical indication and to relate the results to the clinical conditions associated with the removal of these devices. Osteosynthesis plates and screws retrieved from 30 patients between January 2010 and September 2013 were studied by metallographic, gas, and energy dispersive X-ray (EDX) analyses and the medical records of these patients were reviewed. Forty-eight plates and 238 screws were retrieved. The time elapsed between plate and screw insertion and removal ranged between 11 days and 10 years. Metallographic analysis revealed that all the plates were manufactured from commercially pure titanium (CP-Ti). The screw samples analyzed consisted of Ti-6Al-4V alloy, except four samples, which consisted of CP-Ti. Titanium plates studied by EDX analysis presented greater than 99.7% titanium by mass. On gas analysis of Ti-6Al-4V screws, three samples were outside the standard values. One CP-Ti screw sample and one plate sample also presented an oxygen analysis value above the standard. The results indicated that the physical properties and chemical compositions of the plates and screws did not correspond with the need to remove these devices or the time of retention.

Development Plates For Stable Internal Fixation: Study Of Mechanical Resistance In Simulated Fractures Of The Mandibular Condyle.

To develop Y-shaped plates with different thicknesses to be used in simulated fractures of the mandibular condyle. Ten plates were developed in Y shape, containing eight holes, and 30 synthetic polyurethane mandible replicas were developed for the study. The load test was performed on an Instron Model 4411 universal testing machine, applying load in the mediolateral and anterior-posterior positions on the head of the condyle. Two-way ANOVA with Tukey testing with a 5% significance level was used. It was observed that when the load was applied in the medial-lateral plate of greater thickness (1.5 mm), it gave the highest strength, while in the anteroposterior direction, the plate with the highest resistance was of the lesser thickness (0.6 mm). A plate with a thickness of 1.5 mm was the one with the highest average value for all displacements. In the anteroposterior direction, the highest values of resistance were seen in the displacement of 15 mm. After comparing the values of the biomechanical testing found in the scientific literature, it is suggested that the use of Y plates are suitable for use in subcondylar fractures within the limitations of the study.

Mechanical strength and thermal conductivity of low-porosity gypsum plates

The thermal conductivity and mechanical strength of gypsum and gypsum-cellulose plates made from commercial plaster by a new process have been measured. The gypsum parts made by the new process, 'novogesso', have high mechanical strength and low porosity. The gypsum strength derives from both the high aspect ratio of the gypsum crystals and the strong adhesion among them by nano-flat layers of confined water, which behaves as supercooled water. Another contribution to the strength comes from the nano-flatness of the lateral surfaces of the gypsum single crystals. The bending and compression strengths, σB and σc, of gypsum plates prepared by this new technique can be as high as 30 and 100 MPa, respectively. The way gypsum plates have been assembled as well as their low thermal conductivity allowed for the construction of a low-cost experimental house with thermal and acoustic comfort.

A simple procedure for reliability assessment of thin composite plates against buckling

In some circumstances ice floes may be modeled as beams. In general this modeling supposes constant thickness, which contradicts field observations. Action of currents, wind and the sequence of contacts, causes thickness to vary. Here this effect is taken into consideration on the modeling of the behavior of ice hitting inclined walls of offshore platforms. For this purpose, the boundary value problem is first equated. The set of equations so obtained is then transformed into a system of equations, that is then solved numerically. For this sake an implicit solution is developed, using a shooting method, with the accompanying Jacobian. In-plane coupling and the dependency of the boundary terms on deformation, make the problem non-linear and the development particular. Deformation and internal resultants are then computed for harmonic forms of beam profile. Forms of giving some additional generality to the problem are discussed.

Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks

The objective of this work is to present the finite element modeling of laminate composite plates with embedded piezoelectric patches or layers that are then connected to active-passive resonant shunt circuits, composed of resistance, inductance and voltage source. Applications to passive vibration control and active control authority enhancement are also presented and discussed. The finite element model is based on an equivalent single layer theory combined with a third-order shear deformation theory. A stress-voltage electromechanical model is considered for the piezoelectric materials fully coupled to the electrical circuits. To this end, the electrical circuit equations are also included in the variational formulation. Hence, conservation of charge and full electromechanical coupling are guaranteed. The formulation results in a coupled finite element model with mechanical (displacements) and electrical (charges at electrodes) degrees of freedom. For a Graphite-Epoxy (Carbon-Fibre Reinforced) laminate composite plate, a parametric analysis is performed to evaluate optimal locations along the plate plane (xy) and thickness (z) that maximize the effective modal electromechanical coupling coefficient. Then, the passive vibration control performance is evaluated for a network of optimally located shunted piezoelectric patches embedded in the plate, through the design of resistance and inductance values of each circuit, to reduce the vibration amplitude of the first four vibration modes. A vibration amplitude reduction of at least 10 dB for all vibration modes was observed. Then, an analysis of the control authority enhancement due to the resonant shunt circuit, when the piezoelectric patches are used as actuators, is performed. It is shown that the control authority can indeed be improved near a selected resonance even with multiple pairs of piezoelectric patches and active-passive circuits acting simultaneously. (C) 2010 Elsevier Ltd. All rights reserved.