Compressive Strength of Long Rectangular Plates under Hydrostatic Pressure

Okada, Hiroo; Oshima, Koichi; Fukumoto, Yuhshi

doi:10.2534/jjasnaoe1968.1979.146_270

Cited by 12 publications

(7 citation statements)

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“…In this case, Q = 3.7 has no hysteresis while Q = 4 has hysteresis; so the buckling behavior of the plate occurs at between Q = 3.7 and Q = 4. By a refined estimation, we determined that Q * = 3.75 is the buckling critical value detected by the present method, which is very close to the critical value 3.7 given in [Okada et al 1979].…”

Section: 4supporting

confidence: 81%

“…In addition, an external stimulus to the plate may switch the deflection form of the plate when edge pressure is in between load of point A and load of point B, because in this interval (hysteresis area) this system has two stable states either of which is physically realizable. Figure 11 provides the solutions for plates 4 and 5 by the present method and the Rayleigh-Ritz method [Okada et al 1979]. It can be seen that both methods can detect the critical buckling points.…”

Section: 4mentioning

confidence: 95%

“…Then Levy [1944] and Woolley et al [1946] analyzed long rectangular plates with simply supported edges and clamped edges respectively by a similar approach. Okada, Oshima and Fukumoto [Okada et al 1979] applied the Rayleigh-Ritz method to a simply supported long rectangular plate (length/width = 3 and 4) under hydrostatic pressure, and discussed various buckling behaviors. Ueda, Rashed and Paik [Ueda et al 1987] proposed an incremental Galerkin method by solving stepwise the linearized form of the von Kármán plate equations of the simply supported rectangular plate.…”

Section: Introductionmentioning

confidence: 99%

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2014

J. Mech. Mater. Struct.

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The present investigation is concerned with wave propagation at an interface of two different micropolar thermoelastic solid half-spaces with distinct conductive and thermodynamic temperatures. Reflection and transmission phenomena of plane waves impinging obliquely at a plane interface between two different micropolar thermoelastic solid half-spaces with two temperatures are investigated. The incident wave is assumed to be striking at the plane interface after propagating through one of the micropolar generalized thermoelastic solids with two temperatures. Amplitude ratios of the various reflected and transmitted waves are obtained in closed form and it is found that these are functions of the angle of incidence and frequency, and are affected by the elastic properties of the media. Micropolarity and twotemperature effects are shown on these amplitude ratios for a specific model. Results of some earlier workers have also been deduced from the present investigation. 121 122 RAJNEESH KUMAR, MANDEEP KAUR AND SATISH C. RAJVANSHI Chen and Williams [1968] and Chen et al. [1969] formulated a theory of heat conduction in deformable bodies. This depends on two distinct temperatures, the conductive temperature and thermodynamic temperature T . Chen et al. [1969] suggested that the difference between these two temperatures is proportional to the heat supply. These two temperatures may be equal under certain conditions for timeindependent situations. However, for time-dependent problems relating to wave propagation, these two temperatures are, in general, different, regardless of the presence of a heat supply. The two temperatures and the strain are found to have representation in the form of a traveling wave pulse, a response which occurs instantaneously throughout the body [Boley and Tolins 1962]. Warren and Chen [1973] investigated wave propagation in the two-temperature theory of thermoelasticity.Youssef [2006] presented a new theory of generalized thermoelasticity by taking into account the theory of heat conduction in deformable bodies, which depends on distinct conductive and thermodynamic temperatures. He also established a uniqueness theorem for the equation of two-temperature generalized linear thermoelasticity for a homogeneous and isotropic body. Recently, Puri and Jordan [2006] studied the propagation of plane waves under two temperatures. Youssef and Al-Lehaibi [2007] and Youssef and Al-Harby [2007] investigated various problems on the basis of two-temperature thermoelasticity with a relaxation time and showed that the obtained results are qualitatively different when compared to those in the case of one-temperature thermoelasticity. Magaña and Quintanilla [2009] investigated the uniqueness and growth of the solution in two-temperature generalized thermoelastic theories. Mukhopadhyay and Kumar [2009] studied thermoelastic interaction in two-temperature generalized thermoelasticity in an infinite medium with a cylindrical cavity. Various investigators have studied problems in two temperatures, for examp...

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Section: 4supporting

confidence: 81%

Section: 4mentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

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2014

J. Mech. Mater. Struct.

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“…For many years, a significant amount of research has been directed towards the estimation of the ultimate strength of ship bottom plating under combined thrust and lateral pressure [1][2][3][4][5][6][7][8]. In most of these studies, an isolated rectangular plate has been considered assuming simply supported boundaries around the plate.…”

Section: Introductionmentioning

confidence: 99%

Estimation of ultimate strength of continuous stiffened panel under combined transverse thrust and lateral pressure Part 1: Continuous plate

Fujikubo

Yao²,

Khedmati³

et al. 2005

Marine Structures

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A simplified method to estimate the ultimate strength of a continuous plate, typical in ship bottom plating, subjected to combined transverse thrust and lateral pressure is developed. A series of elastic/ elastoplastic large deflection finite element analysis (FEA) of a continuous plate supported along the lines of longitudinal stiffeners and transverse frames is performed. Attention is focused on the effect of a continuity of plating on its buckling and ultimate strengths, while the previous studies are mainly concerned with an isolated plate. Based on the FEA results, a set of formulae has been derived for the estimation of the ultimate strength of a continuous plate under combined transverse thrust and lateral pressure. An increase of elastic buckling strength and a change in the collapse mode from a simply supported mode to a clamped mode are considered as an effect of a continuity of plating. It has been proven from a comparison with FEA that the proposed formulae give very accurate predictions of the ultimate strength. r

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“…Axial load versus deflection: comparison between present method and[Okada et al 1979]: not buckling (plate 4); buckling (plate 5).…”

mentioning

confidence: 99%

Solutions of the von Kármán plate equations by a Galerkin method, without inverting the tangent stiffness matrix

Dai

Yue

Atluri

2014

J. Mech. Mater. Struct.

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Large deflections of a simply supported von Kármán plate with imperfect initial deflections, under a combination of in-plane loads and lateral pressure, are analyzed by a semianalytical global Galerkin method. While many may argue that the dominance of the finite element method in the marketplace may make any other attempts to solve nonlinear plate problems to be redundant and obsolete, semi-and precise analytical methods, when possible, simply serve as benchmark solutions if nothing else. Also, since parametric variations are simpler to access through such analytical methods, they are more useful in studying the physics of the phenomena. In the present method, the Galerkin scheme is first applied to transform the governing nonlinear partial differential equations of the von Kármán plate into a system of general nonlinear algebraic equations (NAEs) in an explicit form. The Jacobian matrix, the tangent stiffness matrix of the system of NAEs, is explicitly derived, which speeds up the Newton-Raphson iterative method if it is used. The present global Galerkin method is compared with the incremental Galerkin method, the perturbation method, the finite element method and the finite difference method in solving the von Kármán plate equations to compare their relative accuracies and efficiencies. Buckling behavior and jump phenomenon of the plate are detected and analyzed. Besides the classical NewtonRaphson method, an entirely novel series of scalar homotopy methods, which do not need to invert the Jacobian matrix (the tangent stiffness matrix), even in an elastostatic problem, and which are insensitive to the guesses of the initial solution, are introduced. Furthermore, we provide a comprehensive review of the newly developed scalar homotopy methods, and incorporate them into a uniform framework, which renders a clear and concise understanding of the scalar homotopy methods. In addition, the performance of various scalar homotopy methods is evaluated through solving the Galerkin-resulting NAEs. The present scalar homotopy methods are advantageous when the system of NAEs is very large in size, when the inversion of the Jacobian may be avoided altogether, when the Jacobian is nearly singular, and the sensitivity to the initially guessed solution as in the Newton-Raphson method needs to be avoided, and when the system of NAEs is either over-or under-determined.

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Compressive Strength of Long Rectangular Plates under Hydrostatic Pressure

Cited by 12 publications

References 0 publications

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Estimation of ultimate strength of continuous stiffened panel under combined transverse thrust and lateral pressure Part 1: Continuous plate

Solutions of the von Kármán plate equations by a Galerkin method, without inverting the tangent stiffness matrix

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