• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.699-702
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• 2000

In order to use a parallel device fur machine tool feed mechanism, it is very important to analyze its stiffness over the workspace. Generally, the stiffness of a rod varies with its length. In this paper, the stiffness of the leg is modeled as a linear function. With the linear stiffness model, the methods that can determine stiffness bounds and max/min stiffness directions are presented utilizing eigenvalues and eigenvectors of the stiffness matrix. The stiffness variation along a tool-path and stiffness mapping over a workspace are presented with cubic-shaped parallel device which is originally designed for machine tool feed mechanism.

• Structural Engineering and Mechanics
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• v.13 no.3
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• pp.299-312
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• 2002

In this paper, a new method to solve the dynamic response problem for structures with interval parameters is presented. It is difficult to obtain all possible solutions with sharp bounds even an optimum scheme is adopted when there are many interval structural parameters. With the interval algorithm, the expressions of the interval stiffness matrix, damping matrix and mass matrices are developed. Based on the matrix perturbation theory and interval extension of function, the upper and lower bounds of dynamic response are obtained, while the sharp bounds are guaranteed by the interval operations. A numerical example, dynamic response analysis of a box cantilever beam, is given to illustrate the validity of the present method.

• Steel and Composite Structures
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• v.5 no.1
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• pp.1-15
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• 2005

Important characteristics of the previously proposed reduced stiffness method and a summery of its design curves for the buckling of the axially loaded sandwich cylindrical shells is presented. Comparison of the lower bound obtained with FEM analysis with that from the reduced stiffness analysis shows that the proposed reduced stiffness method can provide safe lower bounds for the buckling of geometrically imperfect, axially loaded sandwich cylindrical shells. One of the attractive features of the reduced stiffness elastic lower bound analysis is that it provides safe estimates of buckling loads that do not depend on the specification of the precise magnitude of the imperfection spectra. As a result, designers can readily apply this method without being worried about possible geometrical imperfections that might be generated during fabrication and construction of sandwich cylindrical shells.

• Structural Engineering and Mechanics
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• v.51 no.3
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• pp.377-402
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• 2014

In this study, optimal distribution of springs which supports a cantilever beam is investigated to minimize two objective functions defined. The optimal size and location of the springs are ascertained to minimize the tip deflection of the cantilever beam. Afterwards, the optimization problem of springs is set up to minimize the tip absolute acceleration of the beam. The Fourier Transform is applied on the equation of motion and the response of the structure is defined in terms of transfer functions. By using any structural mode, the proposed method is applied to find optimal stiffness and location of springs which supports a cantilever beam. The stiffness coefficients of springs are chosen as the design variables. There is an active constraint on the sum of the stiffness coefficients and there are passive constraints on the upper and lower bounds of the stiffness coefficients. Optimality criteria are derived by using the Lagrange Multipliers. Gradient information required for solution of the optimization problem is analytically derived. Optimal designs obtained are compared with the uniform design in terms of frequency responses and time response. Numerical results show that the proposed method is considerably effective to determine optimal stiffness coefficients and locations of the springs.

• Structural Engineering and Mechanics
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• v.44 no.1
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• pp.73-84
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• 2012

This paper strongly addresses to the problem of the mechanical systems in which parameters are uncertain and bounded. Interval calculation is used to find sharp bounds of the structural parameters for infilled frame system modeled with finite element method. Infill walls are generally treated as non-structural elements considerably to improve the lateral stiffness, strength and ductility of the structure together with the frame elements. Because of their complex nature, they are often neglected in the analytical model of building structures. However, in seismic design, ignoring the effect of infill wall in a numerical model does not accurately simulate the physical behavior. In this context, there are still some uncertainties in mechanical and also geometrical properties in the analysis and design procedure of infill walls. Structural uncertainties can be studied with a finite element formulation to determine sharp bounds of the structural parameters such as wall thickness and Young's modulus. In order to accomplish this sharp solution as much as possible, interval finite element approach can be considered, too. The structural parameters can be considered as interval variables by using the interval number, thus the structural stiffness matrix may be divided into the product of two parts which correspond to the interval values and the deterministic value.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.773-792
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• 2014

In this paper, we study the inverse mode shape problem for an Euler-Bernoulli beam, using an analytical approach. The mass and stiffness variations are determined for a beam, having various boundary conditions, which has a prescribed polynomial second mode shape with an internal node. It is found that physically feasible rectangular cross-section beams which satisfy the inverse problem exist for a variety of boundary conditions. The effect of the location of the internal node on the mass and stiffness variations and on the deflection of the beam is studied. The derived functions are used to verify the p-version finite element code, for the cantilever boundary condition. The paper also presents the bounds on the location of the internal node, for a valid mass and stiffness variation, for any given boundary condition. The derived property variations, corresponding to a given mode shape and boundary condition, also provides a simple closed-form solution for a class of non-uniform Euler-Bernoulli beams. These closed-form solutions can also be used to check optimization algorithms proposed for modal tailoring.

• Smart Structures and Systems
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• v.9 no.4
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• pp.373-392
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• 2012

Tracking control of systems with variable stiffness hysteresis using a gain-scheduled (GS) controller is developed in this paper. Variable stiffness hysteretic system is represented as quasi linear parameter dependent system with known bounds on parameters. Assuming that the parameters can be measured or estimated in real-time, a GS controller that ensures the performance and the stability of the closed-loop system over the entire range of parameter variation is designed. The proposed method is implemented on a spring-mass system which consists of a semi-active independently variable stiffness (SAIVS) device that exhibits hysteresis and precisely controllable stiffness change in real-time. The SAIVS system with variable stiffness hysteresis is represented as quasi linear parameter varying (LPV) system with two parameters: linear time-varying stiffness (parameter with slow variation rate) and stiffness of the friction-hysteresis (parameter with high variation rate). The proposed LPV-GS controller can accommodate both slow and fast varying parameter, which was not possible with the controllers proposed in the prior studies. Effectiveness of the proposed controller is demonstrated by comparing the results with a fixed robust $\mathcal{H}_{\infty}$ controller that assumes the parameter variation as an uncertainty. Superior performance of the LPV-GS over the robust $\mathcal{H}_{\infty}$ controller is demonstrated for varying stiffness hysteresis of SAIVS device and for different ranges of tracking displacements. The LPV-GS controller is capable of adapting to any parameter changes whereas the $\mathcal{H}_{\infty}$ controller is effective only when the system parameters are in the vicinity of the nominal plant parameters for which the controller is designed. The robust $\mathcal{H}_{\infty}$ controller becomes unstable under large parameter variations but the LPV-GS will ensure stability and guarantee the desired closed-loop performance.

• Interaction and multiscale mechanics
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• v.1 no.1
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• pp.103-121
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• 2008

This paper presents an optimization-based method for computing a minimal bounding ellipsoid that contains the set of static responses of an uncertain braced frame. Based on a non-stochastic modeling of uncertainty, we assume that the parameters both of brace stiffnesses and external forces are uncertain but bounded. A brace member represents the sum of the stiffness of the actual brace and the contributions of some non-structural elements, and hence we assume that the axial stiffness of each brace is uncertain. By using the $\mathcal{S}$-lemma, we formulate a semidefinite programming (SDP) problem which provides an outer approximation of the minimal bounding ellipsoid. The minimum bounding ellipsoids are computed for a braced frame under several uncertain circumstances.

• Structural Engineering and Mechanics
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• v.39 no.4
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• pp.541-558
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• 2011

This paper presents an analysis of stochastic eigenvalue problem of plane bar structures. Particular attention is paid to the effect of spatial variations of the flexural properties of the structure on the first four eigenvalues. The problem of spatial variations of the structure properties and their effect on the first four eigenvalues is analyzed in detail. The stochastic eigenvalue problem was solved independently by stochastic finite element method (stochastic FEM) and Monte Carlo techniques. It was revealed that the spatial variations of the structural parameters along the structure may substantially affect the eigenvalues with quite wide gap between the two extreme cases of zero- and full-correlation. This is particularly evident for the multi-segment structures for which technology may dictate natural bounds of zero- and full-correlation cases.

• Structural Engineering and Mechanics
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• v.12 no.4
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• pp.363-376
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• 2001

Sandwich plates are widely used in lightweight design due to their high strength and stiffness to weight ratio. Due to the heterogeneous structure of sandwich plates, they can exhibit local instabilities (wrinkling), which lead to a sudden loss of stiffness in the structure. This paper presents an analytical solution to the wrinkling problem of sandwich plates. The solution is based on the Rayleigh-Ritz method, by assuming an appropriate deformation field. In contrast to the other approaches up to now, this model takes arbitrary and different orthotropic face layers, finite core thickness and orthotropic core material into account. This approach is the first to cover the wrinkling of unsymmetric sandwiches and sandwiches composed of orthotropic FRP face layers, which are most common in advanced lightweight design. Despite the generality of the solution, the computational effort is kept within bounds. The results have been verified using other analytical solutions and unit cell 3D FE calculations.