• 소성∙가공
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• 제8권5호
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• pp.507-519
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• 1999

An approach using the energy method has veen proposed for the analysis of cone spinning having the complicated deformation modes mixed by shear and normal deformation. In the proposed method, the corresponding solution is found through optimization of the total energy dissipation with respect to the parameters assumed by the velocity field defined as the variation of the length in longitudinal direction. The sheet blank is divided into three layers to consider the bending effect and the energy dissipated by shear deformation is superposed to the energy consumption due to normal deformation related with the shrinking deformation is superposed to the energy consumption due to normal deformation related with the shrinking deformation of axi-symmetric sheet element for the evaluation of total deformation energy. In order to check the validity of the proposed method, the complex spinning for making the conical cup is analyzed and the computed results are compared with the experimental results. In comparison of the computed results with existing experimental results,, the good agreement is obtained for the variation of outer radius and the distribution of thickness, and it has thus been shown that the present approach is applicable to the analysis of complex spinning.

• Structural Engineering and Mechanics
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• 제67권3호
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• pp.219-232
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• 2018

This paper deals with the static bending of various types of FGM sandwich plates resting on two-parameter elastic foundations in hygrothermal environment. The elastic foundation is modeled as Pasternak's type, which can be either isotropic or orthotropic and as a special case, it converges to Winkler's foundation if the shear layer is neglected. The present FGM sandwich plate is assumed to be made of a fully ceramic core layer sandwiched by metal/ceramic FGM coats. The governing equations are derived from principle of virtual displacements based on a shear and normal deformations plate theory. The present theory takes into account both shear and normal strains effects, thus it predicts results more accurate than the shear deformation plate theories. The results obtained by the shear and normal deformation theory are compared with those available in the literature and also with those obtained by other shear deformation theories. It is concluded that the present results are slightly deviated from other results because the normal deformation effect is taken into account. Numerical results are presented to show the effects of the different parameters, such as side-to-thickness ratio, foundation parameters, aspect ratio, temperature, moisture, power law index and core thickness on the stresses and displacements of the FG sandwich plates.

• 터널과지하공간
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• 제3권2호
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• pp.142-151
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• 1993

In this study, the deformation characteristics of atrtificially fractured joints of granite under normal and shear loading were investigated. To obtain the characteristics of joint deformation, compression and shear tests were performed in the laboratory on three different sizes of rock specimens. The rock used in the experimens was Iksan granite. Joints were produced artificially by fracturing using the apparatus for generating extension-joint. Joint normal deformability was studied by conducting cyclic loading tests on the joints. Joint closure varied non-linearly with normal stress through cyclic loadings. As normal stress increased, the joints gradually reached a state of maximum joint closure. The relation between normal stress and joint closure for mated and unmated joints was well described by the hyperbolic and exponential function, respectively. Joint shear deformability was studied by performing direct shear tests under normal stresses on the joints. it was shown that the behaviour in the prepeak range was non-linear and joint shear stiffness depended on the size of specimen and the normal stress.

• Structural Engineering and Mechanics
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• 제61권1호
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• pp.49-63
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• 2017

This paper presents an original hyperbolic (first present model) and parabolic (second present model) shear and normal deformation theory for the bending analysis to account for the effect of thickness stretching in functionally graded sandwich plates. Indeed, the number of unknown functions involved in these presents theories is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. It is evident from the present analyses; the thickness stretching effect is more pronounced for thick plates and it needs to be taken into consideration in more physically realistic simulations. The numerical results are compared with 3D exact solution, quasi-3-dimensional solutions and with other higher-order shear deformation theories, and the superiority of the present theory can be noticed.

• Structural Engineering and Mechanics
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• 제51권5호
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• pp.867-891
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• 2014

An equivalent single layer trigonometric shear deformation theory taking into account transverse shear deformation effect as well as transverse normal strain effect is presented for static flexure of cross-ply laminated composite and sandwich plates. The inplane displacement field uses sinusoidal function in terms of thickness coordinate to include the transverse shear deformation effect. The cosine function in thickness coordinate is used in transverse displacement to include the effect of transverse normal strain. The kinematics of the present theory is much richer than those of the other higher order shear deformation theories, because if the trigonometric term (involving thickness coordinate z) is expanded in power series, the kinematics of higher order theories (which are usually obtained by power series in thickness coordinate z) are implicitly taken into account to good deal of extent. Governing equations and boundary conditions of the theory are obtained using the principle of virtual work. The closed-form solutions of simply supported cross-ply laminated composite and sandwich plates have been obtained. The results of present theory are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory.

• 대한수학회지
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• 제46권1호
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• pp.125-150
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• 2009

We analytically construct the versal deformation space of resolution of normal isolated singularities based on the formalism in [9].

• Advances in aircraft and spacecraft science
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• 제3권2호
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• pp.113-148
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• 2016

In a whole variety of higher order plate theories existing in the literature no consideration is given to the transverse normal strain / deformation effects on flexural response when these higher order theories are applied to shear flexible composite plates in view of minimizing the number of unknown variables. The objective of this study is to carry out cylindrical bending of simply supported laminated composite and sandwich plates using sinusoidal shear and normal deformation plate theory. The most important feature of the present theory is that it includes the effects of transverse normal strain/deformation. The displacement field of the presented theory is built upon classical plate theory and uses sine and cosine functions in terms of thickness coordinate to include the effects of shear deformation and transverse normal strain. The theory accounts for realistic variation of the transverse shear stress through the thickness and satisfies the shear stress free conditions at the top and bottom surfaces of the plate without using the problem dependent shear correction factor. Governing equations and boundary conditions of the theory are obtained using the principle of minimum potential energy. The accuracy of the proposed theory is examined for several configurations of laminates under various static loadings. Some problems are presented for the first time in this paper which can become the base for future research. For the comparison purpose, the numerical results are also generated by using higher order shear deformation theory of Reddy, first-order shear deformation plate theory of Mindlin and classical plate theory. The numerical results show that the present theory provides displacements and stresses very accurately as compared to those obtained by using other theories.

• Geomechanics and Engineering
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• 제11권5호
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• pp.671-690
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• 2016

This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.

• 대한수학회지
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• 제40권4호
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• pp.709-725
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• 2003

We give an analytic approach to the versal deformation of a resolution of a germ of normal isolated singularities. In this paper, we treat only formal deformation theory and it is applied to complete the CR-description of the simultaneous resolution of a cone eve. a rational curve of degree n in P$^{n}$ (n $\leq$ 4).

• 한국게임학회 논문지
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• 제10권6호
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• pp.169-178
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• 2010

본 논문은 실시간 응용 프로그램에서 사실적인 금속 재질을 렌더링하기 위한 효과적인 기법을 제안한다. 제안된 기법은 금속면의 미세한 흡집을 표현하기 위해 법선 벡터를 섭동(perturbation)하는 방법을 사용한다. 법선 벡터를 섭동하는 일반적인 방법은 범프(bump) 매핑이나 법선(normal) 매핑 등의 방법을 사용하는 것이다. 그러나 이러한 방식은 이방성 반사 특성을 갖는 표면에서는 사실적인 빛의 산란을 보이지 못한다. 금속 특유의 반사를 표현하기 위해서는 미세면 분포 함수를 이용하여 이방성 반사 특성을 모델링하는 것이 일반적이므로 일반적 법선 섭동만으로는 만족스런 결과를 얻지 못한다. 본 논문은 법선 벡터의 섭동과 함께 미세면 분포 함수를 변형하는 기법을 통해 매우 사실적인 금속면 재질 렌더링이 가능한 기법을 제안한 다. 제안된 기법은 쉽게 GPU 프로그램으로 구현되며, 실시간 환경에서 동작한다.