• Wind and Structures
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• 제25권1호
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• pp.25-38
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• 2017

This study investigates the dynamic analysis of a transversely isotropic thin plate. The plate is made of hyperelastic John's material and its constitutive law is obtained by taken the Frechect derivative of the highlighted energy function with respect to the geometry of deformation. The three-dimensional equation governing the motion of the plate is expressed in terms of first Piola-Kirchhoff's stress tensor. In the reduction to an equivalent two-dimensional plate equation, the obtained model generalizes the classical plate equation of motion. It is obtained that the plate under consideration exhibits harmonic force within its planes whereas this force varnishes in the classical plate model. The presence of harmonic forces within the planes of the considered plate increases the natural and resonance frequencies of the plate in free and forced vibrations respectively. Further, the parameter characterizing the transversely isotropic structure of the plate is observed to increase the plate flexural rigidity which in turn increases both the natural and resonance frequencies. Finally, this study reinforces the view that non-classical models of problems in elasticity provide ample opportunity to reveal important phenomena which classical models often fail to apprehend.

• 대한기계학회논문집
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• 제19권8호
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• pp.1876-1888
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• 1995

In this paper, glass surface-mat reinforced epoxy(G.S.R.E.) is developed, It is assured that the material(G.S.R.E.) can be used as photoelastic model material and it satisfy with the required properties of photoelastic model material. Therefore, the material can be used as model material of transparent photoelastic experiment when we analyze the stress distributions of transversely isotropic material by photoelastic experiment. When we use G.S.R.E. as photoelastic experiment model material, we had better use the G.S.R.E. which fiber volume ratio is less than 0.7% in the high temperature(stress freezing method) and than 1.74% in the room temperature. Relationships between stress fringe value and elastic modulus in transversely isotropic material are developed in this paper, it is assured by experiment that they are established in the room temperature or in the high temperature. Therefore we can obtain stress fringe value or elastic modulus from the relationships between stress fringe value and elastic modulus.

• 터널과지하공간
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• 제18권3호
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• pp.194-201
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• 2008

횡등방성 암석의 인장강도 특성 해석을 위하여 새로운 이방성 인장파괴함수를 제안하였다. 제안된 함수에서 인장강도는 연약면과 수직한 방향에서 최소가 되며 연약면과 평행한 방향쪽으로 지수함수적으로 증가하면서 최대값에 수렴된다. 제안된 이방성 인장파괴함수는 실험적으로 측정이 가능한 3개의 강도정수로 정의된다. 제안된 함수를 임계면법에 적용하여 연약면의 방향성에 따른 횡등방성 암석의 인장강도 및 파괴면의 방향을 탐색할 수 있는 수치해석적 기법을 제시하였다. 문헌에 보고된 횡등방성 암석의 직접인장시험 결과를 모사함으로써 제안된 방법의 적합성을 검토하였다. 수치해석결과와 직접인장시험 결과는 전반적으로 유사한 결과를 보여주었다.

• Journal of applied mathematics & informatics
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• 제6권3호
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• pp.873-884
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• 1999

On the basis of the semi-linear material of John invoking the theory of homogenization for heterogeneous media and the theory of invariants for isotropic scalar functions an energy function is built for a transversely-isotropic medium in finite elastic deformation. The ponyting Effect for material in simple shear is reviewed for this case of transversal isotropy. It is shown that this effect is apprehended by the constructed energy function.

• 터널과지하공간
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• 제15권6호
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• pp.391-399
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• 2005

본 연구에서는 횡등방성 암반에서 이방성 정도에 따른 응력 차와 3차원 주응력 하의 터널방향, 이방성 정도에 따른 터널 단면에서의 2차원 응력 차를 이론적으로 구하였다. 구해진 응력상황 하의 터널에 대하여 $FLAC^{2D}$를 이용하여 이방성 고려여부에 따른 천단, 측벽, 바닥의 응력 차를 비교${\cdot}$검토하였다. 그 결과 이방성을 무시할 경우 응력 조건에 무관하게 주응력의 크기와 방향이 다르게 나타나며, 이방성 정도가 커질수록 응력차가 증가함을 알 수 있다. 이방성의 방향에 따라 응력 차가 달리 나타나며, 특히 이방성의 방향이 x축으로부터 시계반대방향으로 $45^{\circ}$와 $135^{\circ}$에서 가장 큰 응력 차가 발생함을 확인하였다.

• Coupled systems mechanics
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• 제9권4호
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• pp.343-358
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• 2020

The present research deals with the time-harmonic deformation in transversely isotropic magneto thermoelastic solid with two temperature (2T), rotation due to inclined load and laser pulse. Generalized theory of thermoelasticity has been formulated for this mathematical model. The entire thermo-elastic medium is rotating with uniform angular velocity and subjected to thermally insulated and isothermal boundaries. The inclined load is supposed to be a linear combination of a normal load and a tangential load. The Fourier transform techniques have been used to find the solution to the problem. The displacement components, stress components, and conductive temperature distribution with the horizontal distance are computed in the transformed domain and further calculated in the physical domain using numerical inversion techniques. The effect of angle of inclination of normal and tangential load for Green Lindsay Model and time-harmonic source for Lord Shulman model is depicted graphically on the resulting quantities.

• Structural Engineering and Mechanics
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• 제62권6호
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• pp.675-693
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• 2017

In this paper, based on the first-order shear deformation plate theory, buckling analysis of piezoelectric coupled transversely isotropic rectangular plates is investigated. By assuming the transverse distribution of electric potential to be a combination of a parabolic and a linear function of thickness coordinate, the equilibrium equations for buckling analysis of plate with surface bonded piezoelectric layers are established. The Maxwell's equation and all boundary conditions including the conditions on the top and bottom surfaces of the plate for closed and open circuited are satisfied. The analytical solution is obtained for Levy type of boundary conditions. The accurate buckling load of laminated plate is presented for both open and closed circuit conditions. From the numerical results it is found that, the critical buckling load for open circuit is more than that of closed circuit in all boundary and loading conditions. Furthermore, the critical buckling loads and the buckling mode number increase by increasing the thickness of piezoelectric layers for both open and closed circuit conditions.

• Coupled systems mechanics
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• 제8권6호
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• pp.501-522
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• 2019

The present study is concerned with the thermoelastic interactions in a two dimensional axisymmetric problem in transversely isotropic thermoelastic solid using new modified couple stress theory without energy dissipation and with two temperatures. The Laplace and Hankel transforms have been employed to find the general solution to the field equations. Concentrated normal force, normal force over the circular region, concentrated thermal source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. The effect of two temperature varying by taking different values for the two temperature on the components of normal stress, tangential stress, conductive temperature and couple stress are depicted graphically.

• Coupled systems mechanics
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• 제9권5호
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• pp.411-432
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• 2020

This research is devoted to the study of plane wave propagation in homogeneous transversely isotropic (HTI) magneto-thermoelastic rotating medium with combined effect of Hall current and two temperature due to multi-dual-phase lag heat transfer. It is analysed that, for 2-D assumed model, three types of coupled longitudinal waves (quasi-longitudinal, quasi-transverse and quasi-thermal) are present. The wave characteristics like phase velocity, specific loss, attenuation coefficients, energy ratios, penetration depths and amplitude ratios of transmitted and reflected waves are computed numerically and illustrated graphically and compared for different theories of thermoelasticity. Some particular cases are also derived from this research.

• Steel and Composite Structures
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• 제35권3호
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• pp.343-351
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• 2020

The present research deals with the multi-dual-phase-lags thermoelasticity theory for thermoelastic behavior of transversely isotropic thermoelastic thin circular plate The Laplace and Hankel transform techniques have been used to find the solution of the problem. The displacement components, stress components, and conductive temperature distribution are computed in the transformed domain with the radial distance and further determined in the physical domain using numerical inversion techniques. The effect of rotation and two temperature are depicted graphically on the resulting quantities.