• 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.

• Structural Engineering and Mechanics
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• v.43 no.6
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• pp.739-759
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• 2012

The tailoring optimization technique recently developed by the author for improving structural response and energy absorption of composites is extended to sandwich shells using a previously developed zig-zag shell model with hierarchic representation of displacements. The in-plane variation of the stiffness properties of plies and the through-the thickness variation of the core properties are determined solving the Euler-Lagrange equations of an extremal problem in which the strain energy due to out-of-plane strains and stresses is minimised, while that due to their in-plane counterparts is maximised. In this way, the energy stored by unwanted out-of-plane modes involving weak properties is transferred to acceptable in-plane modes. As shown by the numerical applications, the critical interlaminar stress concentrations at the interfaces with the core are consistently reduced without any bending stiffness loss and the strength to debonding of faces from the core is improved. The structural model was recently developed by the author to accurately describe strain energy and interlaminar stresses from the constitutive equations. It a priori fulfills the displacement and stress contact conditions at the interfaces, considers a second order expansion of Lame's coefficients and a hierarchic representation that adapts to the variation of solutions. Its functional d.o.f. are the traditional mid-plane displacements and the shear rotations, so refinement implies no increase of the number of functional d.o.f. Sandwich shells are represented as multilayered shells made of layers with different thickness and material properties, the core being treated as a thick intermediate layer.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.1083-1088
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• 2004

This paper deals with the vibration and stability of a circular cylindrical shaft, modeled as a tapered thin-walled composite beam and spinning with constant angular speed about its longitudinal axis, and subjected to an axial compressive force. Hamilton's principle and the assumed mode method are employed to derive the governing equations of motion. The resulting eigenvalue problem is analyzed, and the stability boundaries are presented for selected taper ratios and axial compressive force combinations. Taking into account the directionality property of fiber reinforced composite materials, it is shown that for a shaft featuring flapwise-chordwise-bending coupling, a dramatic enhancement of both the vibration and stability behavior can be reached. It is found that by the structural tailoring and tapering, bending natural frequencies, stiffness and stability region can be significantly increased over those of uniform shafts made of the same material. In addition, the particular case of a classical beam with internal damping effect is also included.

• Steel and Composite Structures
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• v.42 no.4
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• pp.489-499
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• 2022

This paper proposes a numerical optimization method to design the mesoscale architecture of textile composite for simultaneously enhancing mechanical and thermal properties, which compete with each other making it difficult to design intuitively. The base cell of the periodic warp and fill yarn system is served as the design space, and optimal fibre yarn geometries are found by solving the optimization problem through the proposed method. With the help of homogenization method, analytical formulae for the effective material properties as functions of the geometry parameters of plain-woven textile composites were derived, and they are used to form the inverse homogenization method to establish the design problem. These modules are then put together to form a multiobjective optimization problem, which is formulated in such a way that the optimal design depends on the weight factors predetermined by the user based on the stiffness and thermal terms in the objective function. Numerical examples illustrate that the developed method can achieve reasonable designs in terms of fibre yarn paths and geometries.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.501-507
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• 1997

Composite material has very excellent mechanical properties including tensile stress and specific strength. Especially impact loads may be expected in many of the engineering applications of it. The suitability of composite material for such applications is determined not only by the usual paramenters, but its impactor energy-absorbing properties. Composite material under impact load has poor mechanical behavior and so needs tailoring its structure. Genetic algorithms(GA) is probabilistic optimization technique by principle of natural genetics and natural selection and neural networks(NN) is useful for prediction operation on the basis of learned data. Therefore, This study presents optimization techniques on the basis of genetic algorithms and neural networks to minimum stiffness design of laminated composite material.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.37 no.5
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• pp.641-648
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• 2013

A beam is a major load-carrying member in many engineering structures. Beams with properly designed cross sections and stiffeners are required to enhance the structural properties. Such a design may cause various coupling behaviors, and therefore, an accurate analysis is essential for the proper design of beams. In this research, we manufactured box-beams with stiffeners, which mimic the out-of-plane composite bending-shear coupling behavior reported in literature. A modal test is carried out to obtain the dynamic characteristics, such as natural frequencies and mode shapes, of the box-beam. The obtained results are compared with those of 3D FEM, which confirm that the out-of-plane bending-shear coupling behavior reported in literature is possible. The coupling behavior can be controlled by the proper design of the stiffeners.

• Transactions of Materials Processing
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• v.17 no.8
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• pp.633-642
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• 2008

It's important to measure quantitative properties about thermal-nano behavior of polymer for producing high quality components using Nanoimprint lithography process. Nanoscale indents can be used to make the cells for molecular electronics and drug delivery, slots for integration into nanodevices, and defects for tailoring the structure and properties. In this study, formability of polymethylmetacrylate(PMMA) and polycarbonate(PC) were characterized Polymer has extreme variation in thermo mechanical variation during forming high temperature. Because of heating the polymer, it becomes softer than at room temperature. In this case it is particularly important to study high temperature-induced mechanical properties of polymer. Nanoindenter XP(MTS) was used to measure thermo mechanical properties of PMMA and PC. Polymer was heated by using the heating stage on NanoXP. At CSM(Continuous Stiffness Method) mode test, heating temperature was $110^{\circ}C,120^{\circ}C,130^{\circ}C,140^{\circ}C$ and $150^{\circ}C$ for PMMA, $140^{\circ}C,150^{\circ}C,160^{\circ}C,170^{\circ}C$ and $180^{\circ}C$ for PC, respectively. Maximum indentation depth was 2000nm. At basic mode test, heating temperature was $90^{\circ}C$ and $110^{\circ}C$ for PMMA, $140^{\circ}C,160^{\circ}C$ for PC. Maximum load was 10mN, 20mN and 40mN. Also indented pattern was observed by using SEM and AFM. Mechanical properties of PMMA and PC decreased when temperature increased. Decrease of mechanical properties from PMMA went down rapidly than that of PC.