Mathematical modelling of timber-framed walls using fictive diagonal elements

This paper presents mathematical modelling of timber-framed wall where a braced frame with one fictive diagonal is used. The model is suitable for analysis of lateral loads on the structure. Its advantage compared to other models is its simplicity, the fact that it is easy to use in practise, and its suitability for use with simpler and cheaper programs for static and dynamic analysis. Further numerical calculations were performed, which showed good approximation with experimental studies and with the finite element method. The Tower 6 program for static and dynamic analysis has been used to model timber-framed walls. Appropriate stiffness of timber-framed wall is obtained by varying the cross-section of the fictive diagonal. Because the cross-section of the fictive diagonal is directly connected to the analytical calculation of the stiffness of the timber-framed wall, this model is also able to factor in different spacing distance, different sheathing boards, the appearance of tensile cracks in a sheathing board, as well as walls with glazing or openings.     

Mathematical modelling of a hydraulic accumulator for hydraulic hybrid drives

ABSTRACT

Hydraulic accumulators are used as energy storages in a wide area of applications. In particular, in automotive hybrid drive-trains, this type of energy storage is an interesting alternative to today’s common strategies like chemical batteries or flywheels. This article deals with the mathematical modelling of a hydraulic accumulator for passenger vehicles, which comprises a carbon fibre reinforced plastic (CFRP) body and aluminium piston. The thermodynamical behaviour of the oil and gas as well as the interaction with the CFRP body is investigated in detail. Starting from a complex model, two models of reduced complexity are derived. The validation of these models with measurement data from a test drive with a prototype series hydraulic hybrid drive-train proves their high accuracy.     

Bond-slip behavior of CFRP plate-concrete interface

The paper deals with evaluation of the bond performance between a CFRP plate and concrete with respect to various compressive strengths of concrete and bond lengths of the CFRP plate as parameters. To consider stress conditions in the tensile zone of reinforced concrete (RC) structures, double-lap axial tension tests were conducted for eight specimens with CFRP plates bonded to concrete prisms. In addition, a simple linear bond-slip model for the CFRP plate/concrete joints, developed from the bond tests, was used. To verify the model proposed, a total of seven RC beams were strengthened with CFRP plates and tested in flexure employing various bond lengths, strengthening methods, and numbers of CFRP plates. A nonlinear finite-element analysis, with the bond–slip model incorporated in the DIANA program, was performed for the strengthened RC beams. Also, the results of flexural test and analytical predictions are found to be in close agreement in terms of yield and ultimate loads and ductility.     

Cryogenic mechanical response of multilayer satin weave CFRP composites with cracks

We deal with the thermomechanical response of multilayer satin weave carbon-fiber-reinforced polymer (CFRP) laminates with internal and/or edge cracks and temperature-dependent material properties subjected to tensile loading at cryogenic temperatures. The composite material is assumed to be under the generalized plane strain. Cracks are located in the transverse fiber bundles and extend to the interfaces between two fiber bundles. A finite-element model is employed to study the influence of residual thermal stresses on the mechanical behavior of multilayer CFRP woven laminates with cracks. Numerical calculations are carried out, and Young’s modulus and stress distributions near the crack tip are shown graphically. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 479–492, July–August, 2008.     

Stress-Strain State in the Zone of Load Transfer in a Composite Specimen under Uniaxial Tension

The stress-strain state in the zone of load transfer in a uniaxially stretched specimen made of a unidirectional epoxy carbon-fiber-reinforced plastic (CFRP) is investigated. A parametric analysis of the influence of geometric and mechanical characteristics of the specimen on its stress-strain state is performed by means of finite-element modeling. The parameters allowing us to significantly reduce the dangerous concentration of transverse and tangential stresses are revealed. The mechanical tensile characteristics of a high-strength pultruded unidirectional CFRP are determined experimentally, and the size effect of its strength is estimated.     

Numerical modelling of turbulent flow over rough walls

The numerical simulation of turbulent flow over rough walls was carried out for various types of roughness. The mathematical model was based on the Reynolds averaged Navier-Stokes equations for incompressible flow. The two-equation SST and oneequation Spalart-Allmaras turbulence models were used. Boundary conditions on rough walls were prescribed directly on the wall using the SST model modified to account for wall roughness by Hellsten and Laine (1997) and the SA model modified by Aupoix and Spalart (2003). Turbulence models were tested for the constant pressure turbulent boundary layer on the rough wall formed by commercial abrasive paper and by tightly packed spheres. The effect of wall roughness on the decelerated flow over a smoothly contoured ramp with flow separation was investigated. Obtained results were compared with experimental data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modeling of the Behavior of Concrete Tension Members Reinforced with FRP Rods

The paper is devoted to the analysis of cracking and deformability of concrete tension members reinforced with fiber-reinforced polymer (FRP) rods. A theoretical nonlinear model, derived from a cracking analysis founded on slip and bond stresses, is adopted for evaluating the crack width, crack spacing, and elongation of tension members. The procedure takes into account the local bond-slip law, experimentally determined by means of pullout tests, and allows us to evaluate the influence of tensile stiffening. The analysis is performed with considering all parameters influencing the behavior of tension members, such as the concrete strength, the kind of FRP rebars, the surface treatment of FRP rebars, and the concrete cover thickness. The theoretical predictions are compared with available experimental results, obtained on cylindrical concrete specimens reinforced with carbon FRP (CFRP) rods, and with predictions of the traditional models usually adopted for design purposes.     

Enhanced electroosmotic flow in a nano-channel patterned with curved hydrophobic strips

We consider the electroosmotic flow (EOF) in a nano-channel in which the channel walls are modulated with a periodic array of curved hydrophobic patches. The objective is to achieve an enhanced flow compared to a slit nano-channel. The shape of the hydrophobic strips are considered to be of sinusoidal form, which resembles the situation in which the channel indentations are filled with immiscible nonconducting fluid over which the electrolyte is considered to be in metastable Cassie state. The homogeneous no-slip portions of the channel walls are considered to posses a constant surface-potential (zeta-potential) or constant surface charge density, while the hydrophobic regions are uncharged. A mathematical model based on the Nernst–Planck–Navier-Stokes equations are considered to analyze the present EOF. A coordinate transformation is adopted to map the irregular physical domain to a regular computational domain. A pressure-correction based control volume approach is adopted to solve the governing equations. We have studied the EOF by varying the amplitude of the hydrophobic region. Our results show that an enhancement in EOF compared to a slit-channel is possible when the Debye length is in the order of the channel height. The EOF in the patterned channel varies with the planform length of the hydrophobic region as well as the relative span of the slip and no-slip regions. A comparison with the pressure-driven flow is also presented to analyze the hindrance created by the electric body force of the unbalanced ions.     

Moment redistribution in continuous reinforced concrete beams strengthened with carbon-fiber-reinforced polymer laminates

The results of tests on continuous steel-fiber-reinforced concrete (RC) beams, with and without an external strengthening, are presented. The internal flexural steel reinforcement was designed so that to allow steel yielding before the collapse of the beams. To prevent the shear failure, steel stirrups were used. The tests also included two nonstrengthened control beams; the other specimens were strengthened with different configurations of externally bonded carbon-fiber-reinforced polymer (CFRP) laminates. In order to prevent the premature failure from delamination of the CFRP strengthening, a wrapping was also applied. The experimental results obtained show that it is possible to achieve a sufficient degree of moment redistribution if the strengthening configuration is chosen properly, confirming the results provided by two simple numerical models. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 667–686, September–October, 2007.     

Experimental Investigation of Elastodissipative Characteristics of Carbon-Fiber-Reinforced Plastics

A procedure is described for the experimental study of elastodissipative properties of carbon-fiber-reinforced plastic (CFRP) structures. Experimental values of dissipation factors are given for angle-ply structures with a reinforcing angle varying from 0 to 90°. Elastodissipative characteristics of two types of CFRP are identified. The values obtained can be used for predicting the properties of complex CFRP structures. It is shown that the energy absorption in sandwich structures with CFRP skins and a honeycomb core is mainly governed by properties of the skins.     

Forced stationary gas-structure interaction vibrations in a rectangular parallelepiped tank

A closed rigid rectangular parallelepiped tank is filled with gas and a part of one of its walls is a thin linearly elastic rectangular plate. The problem about the determination of the forced stationary vibrations of the obtained gas–structure interaction system under the action of a source is considered. The method of the crossed strips of Warburton and the Bubnov–Galerkin method are used to create a method of investigation of the dynamic behavior of this gas–structure interaction system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Eulerian‐Lagrangian Concept for the Numerical Simulation of Flat Steady‐State Hot Rolling Processes

For the finite element analysis of stationary flat hot rolling processes, a new and efficient mathematical model was developed. The method is based on an intermediary Eulerian‐Lagrangian concept, where an Eulerian coordinate is employed in the rolling direction, while Lagrangian coordinates are used in the direction of the thickness and width of the strip. This approach yields an efficient algorithm, where the time is eliminated as an independent variable in the steady‐state case. Further, the vector of independent field variables consists of a velocity component in Eulerian and of displacement components in Lagrangian directions. Due to this concept, the free surface deformations can be accounted for directly and the problems encountered with pure Eulerian or Lagrangian models now appear with reduced complexity and can thus be tackled more easily. The general formalism was applied to different practical hot rolling situations, ranging from thick slabs to ultra‐thin hot strips. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An analysis of the joint operation of a CFRP concrete in flexural elements

The strength and fracture mechanism of the contact zone between a carbon-fiber-reinforced plastic (CFRP) and concrete in flexural structural elements is investigated. Two methods for calculating the shear force in the contact zone are considered, one of which takes into account the compliance of the zone and gives results agreeing rather well with experimental data for beams, regardless of the way the CFRP is fastened to concrete. The method of shear stresses is good for beams with in significant shear strains between CFRP and concrete. A method allowing for hardening of the contact zone is suggested. It is shown that the fracture mechanism of the zone depends on the way of fastening the CFRP and the depth the adhesive penetrates into concrete. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 5, pp. 687–700, September–October, 2007.     

Nonstationary fluid‐structure interaction vibrations in a parallelepipedtank

A rigid rectangular parallelepiped tank is filled with a compressible and inviscid fluid as a part of one of its walls is a thin linearly elastic rectangular plate. The problem about the determination of the nonstationary vibrations of the received fluidstructure interaction system is considered. The Laplace transforms, the method of Bubnov‐Galerkin and the method of the crossed strips of G. Warburton are amalgamated to create some fast convergent method to investigate the dynamic behavior of the fluid‐structure interaction system under consideration in the cases of arbitrary supporting conditions of the plate. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The Effect of an Active Diluent on the Properties of Epoxy Resin and Unidirectional Carbon-Fiber-Reinforced Plastics

The influence of an active diluent on the properties of an epoxy matrix and carbon-fiber-reinforced plastics (CFRP) is investigated. The physicomechanical properties of an ED-20 epoxy resin modified with diglycidyl ether of diethylene glycol (DEG-1), the adhesion strength at the epoxy matrix–steel wire interface, and the mechanical properties of unidirectional CFRP are determined. The concentration of DEG-1 was varied from 0 to 50 wt.%. The properties of the matrix, the interface, and the composites are compared. It is stated that the matrix strength affects the strength of unidirectional CFRP in bending and not their strength in tension, compression, and shear. The latter fact seems somewhat unexpected. The interlaminar fracture toughness of the composites investigated correlates with the ultimate elongation of the binder. A comparison between the concentration dependences of adhesion strength and the strength of CFRP shows that the matrices utilized provide such a high interfacial strength that the strength of CFRP no longer depends on the adhesion of its constituents.     

Some integer programs arising in the design of main frame computers

In this paper we describe and discuss a problem that arises in the (global) design of a main frame computer. The task is to assign certain functional units to a given number of so called multi chip modules or printed circuit boards taking into account many technical constraints and minimizing a complex objective function. We describe the real world problem. A thorough mathematical modelling of all aspects of this problem results in a rather complicated integer program that seems to be hopelessly difficult — at least for the present state of integer programming technology. We introduce several relaxations of the general model, which are alsoNP-hard, but seem to be more easily accessible. The mathematical relations between the relaxations and the exact formulation of the problem are discussed as well.On leave from University of São Paulo, Brazil.     

Lubrication approximation of flows of a special class of non-Newtonian fluids defined by rate type constitutive equations

We consider the flow of a rate-type fluid defined by an implicit constitutive equation in a channel with non flat walls. We also assume that the channel characteristic width is small in comparison to the channel length, so that the lubrication approximation can be applied. The model developed is mainly motivated by the evidence that many lubricants seem to be well described by implicit rate type fluid models. The mathematical problem is reduced to an integro-differential equation for the pressure that is solved numerically for several channel profiles.     

Effect of gas seepage on stress-field redistribution in the vicinity of a hole

The effect of gas seepage on the stress-strain state of a coal seam is investigated. The problem of the degassing of coal seams with long holes is discussed. It is established that normal tensile stress components develop with the movement of gas in the vicinity of a hole. For certain ultimate tensile strengths of the coal, this reduces to failure of the walls of the hole, and to the development of dynamic phenomena.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 115–119, 1987.     

On the Free Boundary Conditions for a Dynamic Shell Model Based on Intrinsic Differential Geometry

The mathematical theory behind the modeling of shells is a crucial issue in many engineering problems. Here, the authors derive the free boundary conditions and associated strong form of a dynamic shallow Kirchhoff shell model based on the intrinsic geometry methods of Michael Delfour and Jean-Paul Zolésio. This model relies on the oriented distance function which describes the geometry. This is an extension of the work done in [J. Cagnol, I. Lasiecka, C. Lebiedzik and J.-P. Zolésio (2002). Uniform stability in structural acoustic models with flexible curved walls. J. Differential Equation, 186(1), 88–121.], where the model was derived for clamped boundary conditions only. In the current article, manipulations with the model result in a cleaner form where the displacement of the shell and shell boundary is written explicitly in terms of standard tangential operators.