Beam mechanical properties modeling

The proposed modeling scheme for material mechanical properties can easily be incorporated into structural theory to predict mechanical responses on the structural level using finite element and finite difference methods. On the basis of the mechanical property models for FRP composites proposed herein, further investigations conducted on the mechanical responses of fuU scale cellular GFRP beam and column elements subjected to mechanical loads and reaHstic fire exposure are reviewed in Ghapter 7. 

Temperature-dependant material property models were implemented into stmc-tural theory to establish a mechanical response model for FRP composites under elevated temperatures and fire in this chapter. On the basis of the finite difference method, the modeling mechanical responses were calculated and further vaUdated through experimental results obtained from the exposure of full-scale FRP beam and column elements to mechanical loading and fire for up to 2 h. Because of the revealed vulnerabihty of thermal exposed FRP components in compression, compact and slender specimens were further examined and their mechanical responses and time-to-failure were well predicted by the proposed models. 

Kowsika and Mantena (1996) proposed a statistical test pattern in manufacturing unidirectional graphite-epoxy composite beams using pultrusion. The influences of significant variables of the pultrusion process together with their interactive effects on the dynamic mechanical properties were investigated. Mathematical models were subsequently derived to determine the optimal pultrusion process conditions for improved dynamic mechanical properties of the finished product. 

The mechanical properties of hardened materials are similar to those of ordinary fibre-reinforced composites. They are determined by the quality of the matrix and reinforcement, and the interface layer between these two. Particularly interesting are the improved resistance and toughness against impact loading. Modelling of a reinforced concrete beam strengthened by ferrocement thin plates was presented by Elavenil and Chandrasekar (2007). 

In more recent times, with the use of ion beams to clean the surfaces of ceramic substrates, implantation of ions into the surfaces has been brought about with consequent changes in the mechanical properties of such surfaces, and this can be probed in a nondestructive way by using the ISE following the development of a model such as that which follows. 

The remarkable properties of electrospun CNTs nanocomposites continue to draw attention in the development of multifunctional properties of nanostructures for many applications.. Multiscale model for calculation macroscopic mechanical properties for fibrous sheet is developed. Effective properties of the fiber at microscale determined by homogenization using modified shear-lag model, while on the second stage the point-bonded stochastic fibrous network at macroscale replaced by multilevel finite beam element net. Elastic modulus and Poisson s ratio dependence on CNT volume concentration are calculated. Effective properties fibrous sheet as random stochastic network determined numerically. We conclude that an addition of CNTs into the polymer solution results in significant improvement of rheological and structural properties. 

A real human shin-bone has a highly complex geometry. It consists of several types of substances, for instance, bone tissue and marrow, with very different mechanical properties. The substances are also inhomogeneous, anisotropic, and vast biological variations exist between different individuals. The inhomogeneities of the various substances cannot directly be eliminated in the research object. But when it comes to theoretical and mathematical considerations it is necessary to increase the level of idealization and construct a model object which fits into the theoretical framework. The inhomogeneities must in some way or other be reduced before it is possible to fit the shin-bone into a theoretical framework. In the example under consideration the research object was represented as a so-called Timoschenko beam. Only some of the constitutive properties of the shin-bone were then represented in the model object. They comprised, in the final definition, dynamic and structural properties of a rectilinear, twisted, non uniform Timoschenko beam which was made up of two linearly elastic and transversally isotropic compounds and one perfectly flexible compound (Thomsen 1990). 

The test piece of shin-bone is not a hnman shin-bone. It is a manipulated piece which has been cut out of a real human body and has been modified to such an extent that it is possible to prodnce stable measurements on it. Furthermore, it has been modified in such a way that only certain important features of it, which are related to some of its mechanical properties, have been controlled. The test shinbone, i.e. the research object, is a laboratory artifact. It is a non-fiivial problem how this object is related both to the real human shin-bone, as it exists in a living human being, and to the model object, which is the object that theories are about. Data are produced by making measurements on the research object, i.e. the test shin-bone, but they are interpreted as claims about the idealized model object. They are used to put blood and flesh on the Timoschenko beam, that is, data are reduced in such a way that they can be considered as statements about the dimensions and oscillations... 

Therefore, a fiill understanding of the mechanical properties of the textiles is essential for modeling all the above aspects. The mechanical behavior of the textiles was predicted by a three-dimensional analytical model based on a theory of curved beam. The macroscopic behavior of the monofilament textiles was investigated by taking into consideration a unit cell of the order of the filament diameter (30-70 pm) and assuming the nonlinear constitutive behavior of the fibers obtained by the experiments. 

The unique cellular morphologies of foams play a key role in determining their deformation mechanisms [51. They also allow the development of very simple alternative equations based on the mechanical models of beam theory (a branch of civil engineering) combined with scaling concepts, to estimate both the thermoelastic properties and the strengths of foams. Such simple relationships have been developed for foams manifesting elastomeric, elastic-plastic and elastic-brittle responses to mechanical defonnation. While much of this work has focused on the responses of foams to compressive defonnation because of the special importance of this deformation mode in many applications of foams, the responses of foams to tensile and shear deformation have also been considered within this theoretical framework. 

In the schematic shown in Figure 4.2.10, the RF path is visible between the two signal sources (RF ports) used for extracting the S parameters, and is composed of a length of microstrip transmission line from each port connected to a model for a series-switch plate . Driven by the 6 mechanical wires at each side, which control its position, the switch plate is internally modeled as an equivalent circuit including transmission line, frequency-dependent resistance, and variable capacitance between the conductor on the plate and the underlap of the ends of the microstrip lines separated by the gap for the switch isolation. As with the beams, this model is defined by a complete set of parameters, such as the dimensions and material properties. Parameters can be adjusted quickly to achieve the desired RF performance for different closing states of the electromechanical structure. 

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