• 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.

• 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.

• 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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• 제89권3호
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• pp.225-238
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• 2024

In this paper, a quasi-3D hyperbolic shear deformation theory for the bending responses of a functionally graded (FG) porous micro-beam is based on a modified couple stress theory requiring only one material length scale parameter that can capture the size influence. The model proposed accounts for both shear and normal deformation effects through an illustrative variation of all displacements across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the micro-beam. The effective material properties of the functionally graded micro-beam are assumed to vary in the thickness direction and are estimated using the homogenization method of power law distribution, which is modified to approximate the porous material properties with even and uneven distributions of porosity phases. The equilibrium equations are obtained using the virtual work principle and solved using Navier's technique. The validity of the derived formulation is established by comparing it with the ones available in the literature. Numerical examples are presented to investigate the influences of the power law index, material length scale parameter, beam thickness, and shear and normal deformation effects on the mechanical characteristics of the FG micro-beam. The results demonstrate that the inclusion of the size effects increases the microbeams stiffness, which consequently leads to a reduction in deflections. In contrast, the shear and normal deformation effects are just the opposite.

• Advances in materials Research
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• 제5권4호
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• pp.223-244
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• 2016

In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory 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. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

• Advances in aircraft and spacecraft science
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• 제10권3호
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• pp.281-302
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• 2023

In this paper, bending analysis of exponentially varying functionally graded (FG) plate is presented using trigonometric shear deformation theory (TSDT) considering both transverse shear and normal deformation effects. The in-plane displacement field consists of sinusoidal functions in thickness direction to include transverse shear strains and transverse displacement include the effect of transverse normal strain using the cosine function in thickness coordinate. The governing equations and boundary conditions of the theory are derived using the virtual work principle. System of governing equations, for simply supported conditions, Navier's solution technique is used to obtain results. Plate material properties vary across thickness direction according to exponential distribution law. In the current theory, transverse shear stresses are distributed accurately through the plate thickness, hence obviates the need for a shear correction factor. TSDT results are compared with those from other theories to ensure the accuracy and effectiveness of the present theory. The current theory is in excellent agreement with the semi-analytical theory.

• 터널과지하공간
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• 제17권3호
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• pp.203-215
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• 2007

암반의 역학적 변형거동과 안정성은 불연속면의 역학적 특성에 크게 좌우되기 때문에 터널이나 암반구조물의 안정성 해석 및 설계를 위해서는 반드시 암반 불연속면의 역학적 성질을 규명할 필요가 있다. 지하암반 절리면의 실제 거동을 실내에서 정확히 모사하기 위해 본 연구에서는 일련의 일정 수직강성 조건하 직접 전단시험을 수행하여 초기 수직응력, 전단속도 그리고 절리면의 거칠기가 거친 화강암 절리면의 전단거동특성에 미치는 영향을 살펴보았다. 일정 수직강성 조건에서 거친 암석절리에 대한 시험 결과 전단거동은 일반적으로 1차 정점 전단응력에서의 전단응력 감소 정도에 따라 크게 두 가지 형태의 전단거동을 보이는 것으로 구분되었다. 초기 수직응력이 증가함에 따라 정점 전단변위와 1차 정점 전단응력은 증가하지만 마찰각과 정점 마찰계수의 경우 감소하는 것으로 나타났으며, 전단강성과 평균마찰계수의 경우는 초기 수직응력에 영향을 받지 않는 것으로 나타났다. 거친 절리에 대한 전단속도의 영향은 초기 수직응력이 낮은 경우 일부 전단변수들에서 약간 관찰되었으나 수직응력이 증가함에 따라 대부분의 전단시험 결과변수들에서 전단속도의 영향은 미미하였다. 거칠기에 따른 전단거동의 변화를 분석하였으나 명확한 관련성이 나타나는 경우보다 시료간의 편차가 심한 경우가 많았다.

• Steel and Composite Structures
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• 제19권3호
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• pp.521-546
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• 2015

A new refined hyperbolic shear and normal deformation beam theory is developed to study the free vibration and buckling of functionally graded (FG) sandwich beams under various boundary conditions. The effects of transverse shear strains as well as the transverse normal strain are taken into account. Material properties of the sandwich beam faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending, free vibration and buckling analyses are obtained for simply supported sandwich beams. Illustrative examples are given to show the effects of varying gradients, thickness stretching, boundary conditions, and thickness to length ratios on the bending, free vibration and buckling of functionally graded sandwich beams.

• Steel and Composite Structures
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• 제25권5호
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• pp.603-615
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• 2017

This experimental research presents the seismic performance of steel reinforced high-strength concrete (SRHC) short columns. Eleven SRHC column specimens were tested under simulated earthquake loading conditions, including six short column specimens and five normal column specimens. The parameters studied included the axial load level, stirrup details and shear span ratio. The failure modes, critical region length, energy dissipation capacity and deformation capacity, stiffness and strength degradation and shear displacement of SRHC short columns were analyzed in detail. The effects of the parameters on seismic performance were discussed. The test results showed that SRHC short columns exhibited shear-flexure failure characteristics. The critical region length of SRHC short columns could be taken as the whole column height, regardless of axial load level. In comparison to SRHC normal columns, SRHC short columns had weaker energy dissipation capacity and deformation capacity, and experienced faster stiffness degradation and strength degradation. The decrease in energy dissipation and deformation capacity due to the decreasing shear span ratio was more serious when the axial load level was higher. However, SRHC short columns confined by multiple stirrups might possess good seismic behavior with enough deformation capacity (ultimate drift ratio ${\geq}2.5%$), even though a relative large axial load ratio (= 0.38) and relative small structural steel ratio (= 3.58%) were used, and were suitable to be used in tall buildings in earthquake regions.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2005년도 추계 학술발표회 제17권2호
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• pp.53-56
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• 2005

This paper investigates the effect of ductile deformation behavior of high performance hybrid fiber-reinforced cement composites (HPHFRCCs) on the shear behavior of coupling beams to lateral load reversals. The matrix ductility and the reinforcement layout were the main variables of the tests. Three short coupling beams with two different reinforcement arrangements and matrixes were tested. They were subjected to cyclic loading by a suitable experimental setup. All specimens were characterized by a shear span-depth ratio of 1.0. The reinforcement layouts consisted of a classical scheme and diagonal scheme without confining ties. The effects of matrix ductility on deflections, strains, crack widths, crack patterns, failure modes, and ultimate shear load of coupling beams have been examined. The combination of a ductile cementitious matrix and steel reinforcement is found to result in improved energy dissipation capacity, simplification of reinforcement details, and damage-tolerant inelastic deformation behavior. Test results showed that the HPFRCC coupling beams behaved better than normal reinforced concrete control beams. These results were produced by HPHFRCC's tensile deformation capacity, damage tolerance and tensile strength.