• Structural Engineering and Mechanics
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• 제36권5호
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• pp.545-560
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• 2010

Two or more distinct materials are combined into a single functionally graded material (FGM) where the microstructural composition and properties change gradually. Thermal post-buckling behavior of uniform slender FGM beams is investigated independently using the classical Rayleigh-Ritz (RR) formulation and the versatile Finite Element Analysis (FEA) formulation developed in this paper. The von-Karman strain-displacement relations are used to account for moderately large deflections of FGM beams. Bending-extension coupling arising due to heterogeneity of material through the thickness is included. Simply supported and clamped beams with axially immovable ends are considered in the present study. Post-buckling load versus deflection curves and buckled mode shapes obtained from both the RR and FEA formulations for different volume fraction exponents show an excellent agreement with the available literature results for simply supported ends. Response of the FGM beam with clamped ends is studied for the first time and the results from both the RR and FEA formulations show a very good agreement. Though the response of the FGM beam could have been studied more accurately by FEA formulation alone, the authors aim to apply the RR formulation is to find an approximate closed form post-buckling solutions for the FGM beams. Further, the use of the RR formulation clearly demonstrates the effect of bending-extension coupling on the post-buckling response of the FGM beams.

• Steel and Composite Structures
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• 제38권5호
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• pp.583-597
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• 2021

This article develops a nonclassical model to analyze bending response of squared perforated microbeams considering the coupled effect of microstructure and surface stress under different loading and boundary conditions, those are not be studied before. The corresponding material and geometrical characteristics of regularly squared perforated beams relative to fully filled beam are obtained analytically. The modified couple stress and the modified Gurtin-Murdoch surface elasticity models are adopted to incorporate the microstructure as well as the surface energy effects. The differential equations of equilibrium including the Poisson's effect are derived based on minimum potential energy. Exact closed form solution is obtained for bending behavior of the proposed model considering the classical and nonclassical boundary conditions for both uniformly distributed and concentrated loads. The proposed model is verified with results available in the literature. Influences of the microstructure length scale parameter, surface energy, beam thickness, boundary and loading conditions on the bending behavior of perforated microbeams are investigated. It is observed that microstructure and surface parameters are vital in investigation of the bending behavior of perforated microbeams. The obtained results are supportive for the design, analysis and manufacturing of perforated nanobeams that commonly used in nanoactuators, nanoswitches, MEMS and NEMS systems.

• Structural Engineering and Mechanics
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• 제82권3호
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• pp.313-323
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• 2022

Steel laminated elastomeric bearings are commonly used in bridge structures to control displacements and rotations and transfer forces from the superstructure to the substructure. Proper knowledge of design, fabrication and erection procedures is important to ensure stability and adequate structural performance during the lifetime of the bridge. Difference in elevations sometimes leads to large size gaps between the bearing and the girder which makes the grout thickness that is commonly used for leveling deviate beyond standards. This paper investigates the structural response of High Strength Fiber Reinforced Cementitious (HSFRC) thin plinths that are used to close gaps between bearing pads and precast girders. An experimental program was developed for this purpose where HSFRC plinths of different size were cast and tested under vertical loads that simulate bridge loading in service. The structural performance of the plinths was closely monitored during testing, mainly crack propagation, vertical reaction and displacement. Analytically, the HSFRC plinth was analyzed using the beam on elastic foundation theory as the supporting elastomeric bearing pads are highly compressible. Closed form solutions were derived for induced displacement and forces and comparisons were made between analytical and experimental results. Finally, recommendations were made to facilitate the practical use of HSFRC plinths in bridge construction based on its enhanced load carrying capacity in shear and flexure.

• International Journal of Control, Automation, and Systems
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• 제5권5호
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• pp.547-558
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• 2007

This paper proposes a simpler solution to the stabilization problem of a special class of nonlinear underactuated mechanical systems which includes widely studied benchmark systems like Inertia Wheel Pendulum, TORA and Acrobot. Complex internal dynamics and lack of exact feedback linearizibility of these systems makes design of control law a challenging task. Stabilization of these systems has been achieved using Energy Shaping and damping injection and Backstepping technique. Former results in hybrid or switching architectures that make stability analysis complicated whereas use of backstepping some times requires closed form explicit solutions of highly nonlinear equations resulting from partial feedback linearization. It also exhibits the phenomenon of explosions of terms resulting in a highly complicated control law. Exploiting recently introduced Dynamic Surface Control technique and using control Lyapunov function method, a novel nonlinear controller design is presented as a solution to these problems. The stability of the closed loop system is analyzed by exploiting its two-time scale nature and applying concepts from Singular Perturbation Theory. The design procedure is shown to be simpler and more intuitive than existing designs. Design has been applied to important benchmark systems belonging to the class demonstrating controller design simplicity. Advantages over conventional Energy Shaping and Backstepping controllers are analyzed theoretically and performance is verified using numerical simulations.

• Geomechanics and Engineering
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• 제14권3호
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• pp.233-240
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• 2018

Pullout tests are usually employed to determine the ultimate bearing capacity of reinforced soil, and the load-displacement curve can be obtained easily. This paper presents an analytical solution for predicting the full-range mechanical behavior of a buried planar reinforcement subjected to pullout based on a bi-linear bond-slip model. The full-range behavior consists of three consecutive stages: elastic stage, elastic-plastic stage and debonding stage. For each stage, closed-form solutions for the load-displacement relationship, the interfacial slip distribution, the interfacial shear stress distribution and the axial stress distribution along the planar reinforcement were derived. The ultimate load and the effective bond length were also obtained. Then the analytical model was calibrated and validated against three pullout experimental tests. The predicted load-displacement curves as well as the internal displacement distribution are in closed agreement with test results. Moreover, a parametric study on the effect of anchorage length, reinforcement axial stiffness, interfacial shear stiffness and interfacial shear strength is also presented, providing insights into the pullout behaviour of planar reinforcements of MSE structures.

• Advances in aircraft and spacecraft science
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• 제1권3호
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• pp.253-271
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• 2014

A linearised buckling analysis of thin-walled beams is addressed in this paper. Beam theories formulated according to a unified approach are presented. The displacement unknown variables on the cross-section of the beam are approximated via Mac Laurin's polynomials. The governing differential equations and the boundary conditions are derived in terms of a fundamental nucleo that does not depend upon the expansion order. Classical beam theories such as Euler-Bernoulli's and Timoshenko's can be retrieved as particular cases. Slender and deep beams are investigated. Flexural, torsional and mixed buckling modes are considered. Results are assessed toward three-dimensional finite element solutions. The numerical investigations show that classical and lower-order theories are accurate for flexural buckling modes of slender beams only. When deep beams or torsional buckling modes are considered, higher-order theories are required.

• 한국화재소방학회논문지
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• 제17권2호
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• pp.50-55
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• 2003

The lower flash points for the binary system, n-butanol+n-decane, were measured by Pensky-Martens closed cup tester. The experimental results showed the minimum in the flash point versus composition curve. The experimental data were compared with the values calculated by the reduced model under an ideal solution assumption and the flash point-prediction models based on the Van Laar and Wilson equations. The predictive curve based upon the reduced model deviated form the experimental data for this system. The experimental results were in good agreement with the predictive curves, which use the Van Laar and Wilson equations to estimate activity coefficients. However, the predictive curve of the flash point prediction model based on the Willson equation described the experimentally-derived data more effectively than that of the flash point prediction model based on the Van Laar equation.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.279-290
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• 1996

In the present paper we study the Cauchy problem in a Banach space E for an abstract nonlinear differential equation of form $$\frac{d^2u}{dt^2}=-A{\frac{du}{dt}}+B(t)u+f(t, W)$$ where W=($A_1$(t)u, A_2(t)u)..., A_{\nu}(t)u), A_{i}(t),\;i=1,2,...{\nu}$,(B(t), t{\in}I$=[0, b]) are families of closed operators defined on dense sets in E into E, f is a given abstract nonlinear function on $I{\times}E^{\nu}$ into E and -A is a closed linar operator defined on dense set in e into E which generates a semi-group. Further the existence and uniqueness of the solution of the considered Cauchy problem is studied for a wide class of the families ($A_{i}$(t), i =1.2...${\nu}$), (B(t), $t{\in}I$) An application and some properties are also given for the theory of partial diferential equations.

• Bulletin of the Korean Chemical Society
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• 제12권1호
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• pp.39-47
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• 1991

A cluster made of $N_A,\;N_B\;and\;N_C$ atoms in the x, y and z directions respectively, is treated with Huckel method. We obtain the approximate expressions for the eigenvalues and eigenvectors of f.c.c., b.c.c. and h.c.p. clusters in closed forms. The maximum and minimum values of the band so obtained converge to those derived from the Bloch sum in the limit of infinite extension. For a small cluster (of $9{\times}9{\times}5$ atoms, for instance), LDOS from the analytical (approximate) solution manifests better agreement at the surface, than inside the bulk.

• Structural Engineering and Mechanics
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• 제3권1호
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• pp.61-74
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• 1995

A linearly tapered, doubly symmetric thin-walled closed member, such as power-transmission towers and tourist towers, are often characterized by local variation in mass and/or rigidity, due to additional mass and rigidity. On the preliminary stage of design the closed-form solution is more effective than the finite element method. In order to propose approximate solutions, the discontinuous and local variation in mass and/or rigidity is treated continuously by means of a usable function proposed by Takabatake(1988, 1991, 1993). Thus, a simplified analytical method and approximate solutions for the free and forced transverse vibrations in linear elasticity are demonstrated in general by means of the Galerkin method. The solutions proposed here are examined from the results obtained using the Galerkin method and Wilson-${\theta}$ method and from the results obtained using NASTRAN.