• Structural Engineering and Mechanics
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• v.89 no.2
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• pp.199-211
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• 2024

The loading capacity of engineering structures/components reduces after the initiation and propagation of crack eventually leads to the final failure. Hence, it becomes essential to deal with the crack and its effects at the design and simulation stages itself, by detecting the prone area of the fracture. The phase-field (PF) method has been accepted widely in simulating fracture problems in complex geometries. However, most of the PF methods are formulated with second order continuity theoryinvolving C⁰ continuity. In the present study, PF method based on fourth-order (i.e., higher order) theory, maintaining C¹ continuity has been proposed for ductile fracture simulation. The formulation includes fourth-order derivative terms of phase field variable, varying between 0 and 1. Applications of fourth-order PF theory to ductile fracture simulation resulted in novelty in this area. The proposed formulation is numerically solved using a two-dimensional finite element (FE) framework in 3-layered manner system. The solutions thus obtained from the proposed fourth order theory for different benchmark problems portray the improvement in the accuracy of the numerical results and are well matched with experimental results available in the literature. These results are also compared with second-order PF theory and a comparison study demonstrated the robustness of the proposed model in capturing ductile behaviour close to experimental observations.

• Advances in aircraft and spacecraft science
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• v.7 no.1
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• pp.19-40
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• 2020

In the present study, a fifth-order shear and normal deformation theory using a polynomial function in the displacement field is developed and employed for the static analysis of laminated composite and sandwich simply supported spherical shells subjected to sinusoidal load. The significant feature of the present theory is that it considers the effect of transverse normal strain in the displacement field which is eliminated in classical, first-order and many higher-order shell theories, while predicting the bending behavior of the shell. The present theory satisfies the zero transverse shear stress conditions at the top and bottom surfaces of the shell. The governing equations and boundary conditions are derived using the principle of virtual work. To solve the governing equations, the Navier solution procedure is employed. The obtained results are compared with Reddy's and Mindlin's theory for the validation of the present theory.

• Structural Engineering and Mechanics
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• v.73 no.3
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• pp.259-269
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• 2020

In this paper, bending-stretching analysis of thick functionally graded piezoelectric rectangular plates is studied using the higher-order shear and normal deformable plate theory. On the basis of this theory, Legendre polynomials are used for approximating the components of displacement field. Also, the effects of both normal and shear deformations are encountered in the theory. The governing equations are derived using the principle of virtual work and variational approach. It is assumed that plate is made of piezoelectric materials with functionally graded distribution of material properties. Hence, exponential function is used to modify mechanical and electrical properties through the thickness of the plate. Finally, the effect of material properties, electrical boundary conditions and dimensions are investigated on the static response of plate. Also, it is shown that results of the presented model are close to the three dimensional elasticity solutions.

• Structural Engineering and Mechanics
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• v.61 no.1
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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.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.114-117
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• 2001

A higher order zig-zag plate theory is developed to refine accurately predict fully coupled of the mechanical, thermal, and electric behaviors. Both the displacement and temperature fields through the thickness are constructed by superimposing linear zig-zag field to the smooth globally cubic varying field. Smooth parabolic distribution through the thickness is assumed in the transverse deflection in order to consider transverse normal deformation. Linear zig-zag form is adopted in the electric field. The layer-dependent degrees of freedom of displacement and temperature fields are expressed in terms of reference primary degrees of freedom by applying interface continuity conditions as well as bounding surface conditions of transverse shear stresses and transverse heat flux The numerical examples of coupled and uncoupled analysis are demonstrated the accuracy and efficiency of the present theory. The present theory is suitable for the predictions of fully coupled behaviors of thick smart composite plate under mechanical, thermal, and electric loadings.

• Proceeding of KASS Symposium
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• 2008.05a
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• pp.95-100
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• 2008

A 4-node assumed strain finite element based on higher order shear deformation theory is developed to investigate the behaviours of symmetric and unsymmetric laminated composite plates. The present element is based on Reddy's higher order shear deformation theory so that it can consider the parabolic distribution of shear deformation through plate thickness direction. In particular, assumed strain method is adopted to alleviate the shear locking phenomena inherited plate elements based on higher order shear deformation theory. The present finite element has seven degrees of freedom per node and denoted as HSA4. Numerical examples are carried out for symmetric and unsymmetric laminated composite plate with various thickness values. Numerical results are compared with reference solutions produced by other higher order shear deformation theories.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1314-1322
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• 2000

The acoustic property of reactive type single expansion chamber can be analyzed by traditional plane wave theory. This theory can be applied in low frequency range and has good performance. But this theory can't include higher order modes, therefore another method is essential to analyze acoustic filter in high frequency range. Many researcher suggested the method that can concern higher order modes, and their methods are using mode matching technique. But there is no method that can be applied to the analysis of single expansion chamber with arbitrary inlet/outlet duct position and numbers of higher order modes of inlet/outlet duct and middle chamber. In this paper, the method which can analyze single expansion chamber with arbitrary inlet/outlet duct position and numbers of higher order modes of inlet/outlet duct and middle chamber using fundamental mode matching technique, was suggested and the predictions by this method was compared with those by the finite element method, and the influence of inlet/outlet location to acoustic performance of single expansion chamber is investigated and explained by higher order mode effects.

• Steel and Composite Structures
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• v.19 no.6
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• pp.1333-1354
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• 2015

A higher order analytical solution for static analysis of a truncated conical composite sandwich panel subjected to different loading conditions was presented in this paper which was based on a new improved higher order sandwich panel theory. Bending analysis of sandwich structures with flexible cores subjected to concentrated load, uniform distributed load on a patch, harmonic and uniform distributed loads on the top and/or bottom face sheet of the sandwich structure was also investigated. For the first time, bending analysis of truncated conical composite sandwich panels with flexible cores was performed. The governing equations were derived by principle of minimum potential energy. The first order shear deformation theory was used for the composite face sheets and for the core while assuming a polynomial description of the displacement fields. Also, the in-plane hoop stresses of the core were considered. In order to assure accuracy of the present formulations, convergence of the results was examined. Effects of types of boundary conditions, types of applied loads, conical angles and fiber angles on bending analysis of truncated conical composite sandwich panels were studied. As, there is no research on higher order bending analysis of conical sandwich panels with flexible cores, the results were validated by ABAQUS FE code. The present approach can be linked with the standard optimization programs and it can be used in the iteration process of the structural optimization. The proposed approach facilitates investigation of the effect of physical and geometrical parameters on the bending response of sandwich composite structures.

• Advances in materials Research
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• v.5 no.4
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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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• v.3 no.2
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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.