• Smart Structures and Systems
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• v.4 no.2
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• pp.171-182
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• 2008

In this paper, a methodology for the estimation of masonry elasticity and shear moduli is presented, for linear elasticity considerations. The methodology is based on the assumption that for a "periodic" masonry wall, which is formed by the repetition of a basic unit containing blocks and mortar, the mechanical characteristics of the unit are representative of the characteristics of the entire wall. For their calculation, the finite element analysis method is used. A micro-model with finite elements simulating separately the blocks and the mortar is developed. An equivalent finite element model, using an homogenous material is also developed and assuming equivalence of strains for the two models, the homogenous material properties are estimated. The efficiency of the method and its applicability limits are investigated.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.193-212
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• 2004

A new model of generalized thermoelasticity equations for isotropic media with temperature-dependent mechanical properties is established. The modulus of elasticity is taken as a linear function of reference temperature. The present model is described both generalizations, Lord Shulman (L-S) theory with one relaxation time and Green-Lindsay (G-L) with two relaxation times, as well as the coupled theory, instantaneously. The method of the matrix exponential, which constitutes the basis of the state space approach of modern control theory, applied to two-dimensional equations. Laplace and Fourier integral transforms are used. The resulting formulation is applied to a problem of a thick plate subject to heating on parts of the upper and lower surfaces of the plate that varies exponentially with time. Numerical results are given and illustrated graphically for the problem considered. A comparison was made with the results obtained in case of temperature-independent modulus of elasticity in each theory.

• Fire Science and Engineering
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• v.29 no.1
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• pp.1-6
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• 2015

In this study, the damages of high strength concrete exposed to high temperature have been evaluated by the impact echo method. Elastic wave velocity and dynamic modulus of elasticity were measured by the impact echo method, and the compressive strength and the static modulus of elasticity were measured by the compression testing method after exposure to high temperature. The results showed that elastic wave velocity has a linear correlation with the compressive strength and dynamic modulus of elasticity has a linear correlation with static modulus of elasticity. Based on results, it is concluded that the impact echo method can be effectively applied to evaluate the mechanical properties of fire damaged high strength concrete.

• Advances in nano research
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• v.15 no.3
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• pp.215-224
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• 2023

Nonlinearity plays an important role in control systems and the application of design. For this reason, in addition to linear vibrations, nonlinear vibrations of the stepped nanobeam are also discussed in this manuscript. This study investigated the vibrations of stepped nanobeams according to Eringen's nonlocal elasticity theory. Eringen's nonlocal elasticity theory was used to capture the nanoscale effect. The nanoscale stepped Euler Bernoulli beam is considered. The equations of motion representing the motion of the beam are found by Hamilton's principle. The equations were subjected to nondimensionalization to make them independent of the dimensions and physical structure of the material. The equations of motion were found using the multi-time scale method, which is one of the approximate solution methods, perturbation methods. The first section of the series obtained from the perturbation solution represents a linear problem. The linear problem's natural frequencies are found for the simple-simple boundary condition. The second-order part of the perturbation solution is the nonlinear terms and is used as corrections to the linear problem. The system's amplitude and phase modulation equations are found in the results part of the problem. Nonlinear frequency-amplitude, and external frequency-amplitude relationships are discussed. The location of the step, the radius ratios of the steps, and the changes of the small-scale parameter of the theory were investigated and their effects on nonlinear vibrations under simple-simple boundary conditions were observed by making comparisons. The results are presented via tables and graphs. The current beam model can assist in designing and fabricating integrated such as nano-sensors and nano-actuators.

• Computers and Concrete
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• v.22 no.6
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• pp.539-550
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• 2018

Concrete is highly non-linear material which is originating from the transition zone in the form of micro-cracks, governs material response under various loadings. In this paper, the constitutive models published by many researchers have been used to generate novel stiffness parameters and constitutive curves for concrete. Following such linear material formulations, where the energy is conservative during the curvature, and a nonlinear contribution to the concrete has been made and investigated. In which, nonlinear concrete elastic modulus modeling has been developed that is capable-of representing concrete elasticity for grades ranging from 10 to 140 MPa. Thus, covering the grades range of concrete up to the ultra-high strength concrete, and replacing many concrete models that are valid for narrow ranges of concrete strength grades. This has been followed by the introduction of the nonlinear Hooke's law for the concrete material through the replacement of the Young constant modulus with the nonlinear modulus. In addition, the concept of concrete elasticity index (${\varphi}$) has been proposed and this factor has been introduced to account for the degradation of concrete stiffness in compression under increased loading as well as the multi-stages micro-cracking behavior of concrete under uniaxial compression. Finally, a sub-routine artificial neural network model has been developed to capture the concrete behavior that has been introduced to facilitate the prediction of concrete properties under increased loading.

• Structural Engineering and Mechanics
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• v.60 no.4
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• pp.707-727
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• 2016

In this paper, thermal vibration of a nonlocal functionally graded (FG) plates with arbitrary boundary conditions under linear and non-linear temperature fields is explored by developing a refined shear deformation plate theory with an inverse cotangential function in which shear deformation effect was involved without the need for shear correction factors. The material properties of FG nanoplate are considered to be temperature-dependent and graded in the thickness direction according to the Mori-Tanaka model. On the basis of non-classical higher order plate model and Eringen's nonlocal elasticity theory, the small size influence was captured. Numerical examples show the importance of non-uniform thermal loadings, boundary conditions, gradient index, nonlocal parameter and aspect and side-to-thickness ratio on vibrational responses of size-dependent FG nanoplates.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.10a
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• pp.16-23
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• 1997

The Reproducing Kernel Particle Method (RKPM), one of the popular meshless methods, is developed and applied to stress concentration problems. Since the meshless methods require only a set of particles (or nodes) and the description of boundaries in their formulation, the adaptivity can be implemented with much more ease than finite element method. In addition, due to its intrinsic property of multiresolution, the shape function of RKPM provides us a new criterion for adaptivity. Recently, this multiple scale Reproducing Kernel Particle Method and its adaptive procedure have been formulated for large deformation problems by the authors. They are also under development for damage materials and localization problems. In this paper the multiple scale RKPM for linear elasticity is presented and the adaptive procedure is applied to stress concentration problems. Therefore, this work may be regarded as the edition of linear elasticity in the complete framework of multiple scale RKPM and the associated adaptivity.

• Structural Engineering and Mechanics
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• v.77 no.4
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• pp.535-547
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• 2021

This paper concerns with free torsional vibration analysis of size dependent circular nanobars with von kármán type nonlinearity. Although review of the literature suggests several studies employing nonlocal elasticity theory to investigate linear torsional behavior, linear/nonlinear transverse vibration and buckling of the nanoscale structures, so far, no study on the nonlinear torsional behavior of the nanobars, considering the size effect, has been reported. This study employs nonlocal elasticity theory along with a variational approach to derive nonlinear equation of motion of the nanobar. Then, the nonlinear equation is solved using the elliptic functions to extract the natural frequencies of the structure under fixed-fixed and fixed-free end conditions. Finally, the natural frequencies of the nanobar under different nanobar lengths, diameters, nonlocal parameters, and amplitudes of vibration are reported to illustrate the effect of these parameters on the vibration characteristics of the nanobars. In addition, the phase plane diagrams of the nanobar for various cases are reported.

• Journal of the Korean Wood Science and Technology
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• v.44 no.1
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• pp.1-8
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• 2016

Non-destructive ultrasonic testing was applied to evaluate the performance of wood deck material with hole as artificial defect. Ultrasonic velocities and modulus of elasticity were measured according to different diameters and numbers of holes, and comparative analysis to each data were done. From the results, ultrasonic velocities and modulus of elasticity decreased with an increase in the hole size and showed a negative linear correlation with the size of hole, respectively. As the hole size increased, ultrasonic velocities decreased, but their difference was small in the case of the hole size under 15 mm. Also, ultrasonic velocities and modulus of elasticity decreased with increasing the number of holes and showed a strong negative linear correlation to the number of holes. As the number of holes increased, ultrasonic velocities decreased to 3.5%, but modulus of elasticity decreased to 27%. Therefore, the number of holes showed greater influence to modulus of elasticity than ultrasonic velocity. Overall, the size and number of holes influenced to ultrasonic velocity and modulus of elasticity, and their influence will be greater as the size and number of holes increases. These results suggested that several ultrasonic parameters rather than a single ultrasonic velocity should be applied to detect small defects in wood decking materials.

• Structural Engineering and Mechanics
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• v.26 no.5
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• pp.591-615
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• 2007

An improvement is introduced to solve the plane problems of linear elasticity by reciprocal theorem for orthotropic materials. This method gives an integral equation with complex kernels which will be solved numerically. An artificial boundary is defined to eliminate the singularities and also an algorithm is introduced to calculate multi-valued complex functions which belonged to the kernels of the integral equation. The chosen sample problem is a plate, having a circular or elliptical hole, stretched by the forces parallel to one of the principal directions of the material. Results are compatible with the solutions given by Lekhnitskii for an infinite plane. Five different orthotropic materials are considered. Stress distributions have been calculated inside and on the boundary. There is no boundary layer effect. For comparison, some sample problems are also solved by finite element method and to check the accuracy of the presented method, two sample problems are also solved for infinite plate.