• Steel and Composite Structures
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• 제29권1호
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• pp.39-51
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• 2018

Position of a circular or elliptical cutout within an orthotropic plate has great influence on its buckling behavior. This paper aims at finding the optimal position (both location and orientation) of a single circular/elliptical cutout, within an orthotropic rectangular plate, that maximizes the critical buckling load. We consider linear buckling of simply supported orthotropic plates under uniaxial edge loads. To obtain the optimal positions of the cutouts, we have employed a MATLAB optimization routine coupled with buckling computation in ANSYS. Our results show that the position of the cutout that maximizes the buckling load has great dependence on the material properties, laminate configurations, and the geometrical parameters of the plate. These optimal results, for a number of plate geometries and cutout sizes, are reported in this paper. These results will be useful in the design of perforated orthotropic plates against buckling failure.

• Structural Engineering and Mechanics
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• 제75권2호
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• pp.157-174
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• 2020

In the present paper, a simple analytical model is developed based on a new refined parabolic shear deformation theory (RPSDT) for free vibration and buckling analysis of orthotropic rectangular plates with simply supported boundary conditions. The displacement field is simpler than those of other higher-order theories since it is modeled with only two unknowns and accounts for a parabolic distribution of the transverse shear stress through the plate thickness. The governing differential equations related to the present theory are obtained from the principle of virtual work, while the solution of the eigenvalue problem is achieved by assuming a Navier technique in the form of a double trigonometric series that satisfy the edge boundary conditions of the plate. Numerical results are presented and compared with previously published results for orthotropic rectangular plates in order to verify the precision of the proposed analytical model and to assess the impacts of several parameters such as the modulus ratio, the side-to-thickness ratio and the geometric ratio on natural frequencies and critical buckling loads. From these results, it can be concluded that the present computations are in excellent agreement with the other higher-order theories.

• 한국강구조학회 논문집
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• 제19권2호
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• pp.161-170
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• 2007

본 연구에서는 직교이방성 판 해석의 정확도 문제를 개선하기 위하여 평강 리브를 갖는 보강판에 대하여 리브 제원을 고려한 직교이방성 휨 강성 수정 계수를 제안하고자 하였다. 이를 위하여 먼저, 직교이방성 휨 강성과 최대 처짐에 대하여 보강판 제원에 따른 민감도 분석을 실시하였으며, 보강판의 직교이방성 휨 강성 수정 계수에 대한 매개변수 연구를 수행하였다. 연구 결과, 수정 계수의 비율은 판 두께와 상관없이 리브 높이, 간격, 두께별로 하나의 함수로 표현 가능함을 알 수 있었으며, 이러한 수정 계수의 비율 함수로부터 간편하게 수정 휨 강성을 산정할 수 있음을 알 수 있었다. 지지 조건, 변장비, 리브 배치 및 재하 크기가 다른 여러 가지 보강판에 계수 함수를 적용한 결과, 참고 문헌에 비하여 직교이방성 판 해석의 정확도가 향상됨을 알 수 있었다. 따라서, 본 연구에서 제안한 계수 함수식을 사용하면 평강 리브를 갖는 보강판의 직교이방성 판 해석 시 간편하게 상당한 정확도의 결과를 얻을 수 있을 것으로 판단된다.

• 한국농공학회:학술대회논문집
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• 한국농공학회 1999년도 Proceedings of the 1999 Annual Conference The Korean Society of Agricutural Engineers
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• pp.258-264
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• 1999

In this study, a computer program was developed for analysis of the orthotropic curved ring sector plates. In the developing program , the thin-plate theory and multi-base coordinate system was adopted. The effect of design factors-boundary conditions, loading conditions, steel ratio, open angle, radius of curvature and relative flexural rigidity between slab and edge-beam-on the behavior of the circular ring sector plates were discussed. Also, the practical limitations was proposed to replace the problem of the orthotropic sector plate by equivalent rectangular plage.

• Structural Engineering and Mechanics
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• 제4권5호
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• pp.541-552
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• 1996

This paper is concerned with the structural optimization problem of maximizing the compressive buckling load of orthotropic rectangular plates for a given volume of material. The optimality condition is first derived via variational calculus. It states that the thickness distribution is proportional to the strain energy density contrary to popular claims of constant strain energy density at the optimum. An engineers physical meaning of the optimality condition would be to make the average strain energy density with respect to the depth a constant. A double cosine thickness varying plate and a double sine thickness varying plate are then fine tuned in a one parameter optimization using the Rayleigh-Ritz method of analysis. Results for simply supported square plates indicate an increase of 89% in capacity for an orthotropic plate having 100% of its fibers in $0^{\circ}$ direction.

• Structural Engineering and Mechanics
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• 제39권1호
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• pp.115-123
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• 2011

The present work deals with obtaining the critical buckling load and the natural frequencies of clamped, orthotropic, rectangular thin plates subjected to different linear distributed in-plane forces. An analytical solution is proposed. Using the Ritz method, the dependence between in-plane forces and natural frequencies are estimated for various plate sizes, and some results are compared with finite element solutions and where possible, comparison is made with previously published results. Beam functions are used as admissible functions in the Ritz method.

• Structural Engineering and Mechanics
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• 제7권1호
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• pp.53-67
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• 1999

The natural frequencies and modes of free vibration of specially orthotropic elliptic and circular plates are analysed using the Rayleigh-Ritz method. The assumed functions used are two-dimensional boundary characteristic orthogonal polynomials which are generated using the Gram-Schmidt orthogonalization procedure. The first five natural frequencies are reported here for various values of aspect ratio of the ellipse. Results are given for various boundary conditions at the edges i.e., the boundary may be any of clamped, simply-supported or fret. Numerical results are presented here for several orthotropic material properties. For rectilinear orthotropic circular plates, a few results are available in the existing literature, which are compared with the present results and are found to be in good agreement.

• Structural Engineering and Mechanics
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• 제7권5호
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• pp.503-512
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• 1999

Practicing a hole or an orifice through a plate or a slab constitutes a very frequent engineering situation due to operational reasons imposed on the structural system. From a designer's viewpoint it is important to know the effect of this modification of the mechanical system upon its elastodynamic characteristics. The present study deals with the determination of the lower natural frequencies of the structural element described in the title of the paper using a variational approach and expressing the displacement amplitude of the plate in terms of the double Fourier series which constitutes the classical, exact solution when the structure is simply supported at its four edges.

• 대한조선학회지
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• 제24권3호
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• pp.35-42
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• 1987

For the analysis of natural vibrations of a rectangular stiffened plate with inner cutouts, an application of the Rayleigh-Ritz method is investigated. In construction of the trial function for the Rayleigh quotient, only the outer boundary conditions are satisfied with combination of Euler beam functions. As to the modeling of stiffened plates for the energy calculations, a lumping stiffener-effects method and the orthotropic plate analogy are considered for the purpose of comparison. Some numerical results obtained by the Rayleigh-Ritz method are compared with results by experiments and the finite element method. The following are major conclusions; (1) With the lumping stiffener-effects modeling the Rayleigh-Ritz method gives good results of both natural frequencies and mode shapes. The orthotropic plate analogy in cases of regularly stiffened plates is of restrictive use i.e. acceptable for a small cutout. (2) The natural frequency of a stiffened plate with inner cutouts between stiffeners is higher than that of without cutouts and increase as the hole area ratio increases as long as there are no discontinuous stiffeners due to the cutout.

• 동력기계공학회지
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• 제16권6호
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• pp.38-44
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• 2012

In this paper, the bending characteristics of the corrugated plates is analyzed. The trapezoidally, triangularlly and sinusoidally corrugated plates are considered. The corrugated plate is treated as an orthotropic plate that has different flexural properties in two perpendicular directions. The equivalent bending and twisting rigidities for the equivalent orthotropic plates are derived. The equivalent flexural rigidities are estimated under the following postulations: (1) The angle of continuously corrugated plate is not changed after the deformation. (2) When the pure bending moment is applied in corrugated direction of the plate, the its plane is in pure bending. Several numerical examples are analyzed with the proposed method and compared with published results.