Applications of the symplectic method in quasi-static analysis for viscoelastic functionally graded materials

2017 ◽  
Vol 34 (4) ◽  
pp. 1314-1331 ◽  
Author(s):  
W.X. Zhang ◽  
R.G. Liu ◽  
Y. Bai
Keyword(s):  
Functionally Graded Materials ◽  
Correspondence Principle ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Form Solution ◽  
Functionally Graded ◽  
Symplectic Method ◽  
Graded Materials ◽  
Content Type ◽  
Displacement Constraints

Purpose For general quasi-static problems of viscoelastic functionally graded materials (VFGMs), the correspondence principle can be applied only for simple structures with a closed form solution of the corresponding elastic problem exists. In this paper, a new symplectic approach, according to the correspondence principle between linearly elastic and viscoelastic solids, is proposed for quasi-static VFGMs. Design/methodology/approach Firstly, by employing the method of separation of variables, all the fundamental eigenvectors of the governing equations are obtained analytically. Then, the satisfactions of boundary conditions prescribed on the ends and laterals are discussed based on the variable substitution and the eigenvector expansion methods. Findings In the numerical examples, some boundary condition problems are given. The results show the local effects due to the displacement constraints. Originality/value The paper provides an innovative technique for quasi-static problems of VFG Ms. Its correctness and the efficiency are well suported by numerical results.

scholarly journals Free vibrations of planar serial frame structures in the case of axially functionally graded materials

2020 ◽  
pp. 17-17
Author(s):  
Aleksandar Obradovic ◽  
Slavisa Salinic ◽  
Aleksandar Tomovic
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Functionally Graded Materials ◽  
Separation Of Variables ◽  
Closed Form Solution ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Frame Structures ◽  
Variable Cross ◽  
Graded Materials

This paper considers the problem of modal analysis and finding the closed-form solution to free vibrations of planar serial frame structures composed of Euler-Bernoulli beams of variable cross-sectional geometric characteristics in the case of axially functionally graded materials. Each of these beams is performing coupled axial and bending vibrations, where coupling occurs due to the boundary conditions at their joints. The numerical procedure for solving the system of partial differential equations, after the separation of variables, is reduced to solving the two-point boundary value problem of ordinary linear differential equations with nonlinear coefficients and linear boundary conditions. In this case, it is possible to transfer the boundary conditions and reduce the problem to the Cauchy initial value problem. Also, it is possible to analyze the influence of different parameters on the structure dynamic behavior. The method is applicable in the case of different boundary conditions at the right and left ends of such structures, as illustrated by an appropriate numerical example.

The Elastic-Viscoelastic Correspondence Principle for Functionally Graded Materials, Revisited

2003 ◽  
Vol 70 (3) ◽  
pp. 359-363 ◽  
Author(s):  
S. Mukherjee ◽  
Glaucio H. Paulino
Keyword(s):  
Functionally Graded Materials ◽  
Functionally Graded Material ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Graded Materials ◽  
One Dimensional ◽  
Space And Time ◽  
Graded Material ◽  
Nonhomogeneous Materials ◽  
Exponentially Graded

Paulino and Jin [Paulino, G. H., and Jin, Z.-H., 2001, “Correspondence Principle in Viscoelastic Functionally Graded Materials,” ASME J. Appl. Mech., 68, pp. 129–132], have recently shown that the viscoelastic correspondence principle remains valid for a linearly isotropic viscoelastic functionally graded material with separable relaxation (or creep) functions in space and time. This paper revisits this issue by addressing some subtle points regarding this result and examines the reasons behind the success or failure of the correspondence principle for viscoelastic functionally graded materials. For the inseparable class of nonhomogeneous materials, the correspondence principle fails because of an inconsistency between the replacements of the moduli and of their derivatives. A simple but informative one-dimensional example, involving an exponentially graded material, is used to further clarify these reasons.

Modeling of functionally graded materials to estimate effective thermo-mechanical properties

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Royal Madan ◽  
Shubhankar Bhowmick
Keyword(s):  
Experimental Data ◽  
Functionally Graded Materials ◽  
Coefficient Of Thermal Expansion ◽  
Functionally Graded ◽  
Graded Materials ◽  
Content Type ◽  
Wide Range ◽  
Metal Metal ◽  
Novel Material ◽  
First Time

Purpose Functionally graded materials are a special class of composites in which material are graded either continuously or layered wise depending upon its applications. With such variations of materials, the properties of structure vary either lengthwise or thickness wise. This paper aims to investigate models for effective estimation of material properties, as it is necessary for industries to identify the properties of composites or functionally graded materials (FGM’s) before manufacturing and also to develop novel material combinations. Design/methodology/approach Available models were compared for different material combinations and tested with experimental data for properties such as Young’s modulus, density, coefficient of thermal expansion (CTE) and thermal conductivity. Combinations of metal–ceramic and metal–metal were selected such that their ratios cover a wide range of materials. Findings This study reveals different models will be required depending on the material used and properties to be identified. Practical implications The results of the present work will help researchers in the effective modeling of composites or FGM’s for any analysis. Originality/value This paper presents a comparison and review of various analytical methods with experimental data graphically to find out the best suitable method. For the first time, the Halpin-Tsai model was extended in the analysis of the CTE which shows good approximations.

scholarly journals A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Shi-Chao Yi ◽  
Lin-Quan Yao ◽  
Bai-Jian Tang
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Higher Order ◽  
Form Solution ◽  
Functionally Graded ◽  
The Novel ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

Toolpaths for additive manufacturing of functionally graded materials (FGM) parts

2014 ◽  
Vol 20 (6) ◽  
pp. 511-522 ◽  
Author(s):  
Pierre Muller ◽  
Jean-Yves Hascoet ◽  
Pascal Mognol
Keyword(s):  
Additive Manufacturing ◽  
Path Planning ◽  
Functionally Graded Materials ◽  
Process Modeling ◽  
Functionally Graded ◽  
System Control ◽  
Graded Materials ◽  
Content Type ◽  
Manufacturing Procedure ◽  
Selection Of

Purpose – The purpose of this paper is to propose an evaluation of toolpaths for additive manufacturing of functionally graded materials (FGM) parts to ensure the manufacturing of parts in compliance with the desired material distribution. The selection of an appropriate path strategy is critical when manufacturing FGM parts. Design/methodology/approach – The selection of a path strategy is based on a process modeling and an additive laser melting (ALM) system control. To do that, some path strategies are selected, simulated and compared. Findings – The comparison of some paths strategies was applied on a study case from the biomedical field. Test-parts were manufactured and analyzed. Results show a good correlation between the simulated and the deposited material distributions. The evaluation of toolpaths based on the process modeling and the system control was validated. Originality/value – Nowadays, FGM parts manufactured with ALM processes are not functional. To move from these samples to functional parts, it is necessary to have a global approach of the manufacturing procedure centered on the path planning. Few methodologies of path planning are adapted to FGM parts but are still limited.

Slice data representation and format for multi-material objects for additive manufacturing processes

2017 ◽  
Vol 23 (1) ◽  
pp. 149-161 ◽  
Author(s):  
Zhengyan Zhang ◽  
Sanjay Joshi
Keyword(s):  
Additive Manufacturing ◽  
Functionally Graded Materials ◽  
Tool Path ◽  
Heterogeneous Material ◽  
Data Representation ◽  
Functionally Graded ◽  
Material Object ◽  
Graded Materials ◽  
Content Type ◽  
Wide Range

Purpose This paper aims to develop a slice-based representation of geometry and material information of a multi-material object to be produced by additive manufacturing. Representation of complex heterogeneous material allowing for the additive manufacturing-based build of a wide range of objects that are limited only by the constraints of the manufacturing process. Design/methodology/approach Initial 3D CAD models are created with multiple and functionally graded materials using an assembly model to create a single part with well-defined material regions. These models are then sliced to create the geometry and material boundaries required for each layer to enable layer-by-layer fabrication. Findings A representation schema is proposed to add multi-material attributes to a sliced file for additive manufacturing using the combination of material index and material geometry region. A modified common layer interface data format is proposed to allow for representation of a wide range of homogeneous and heterogeneous material for each slice. This format allows for a generic input for tool paths to be generated for each material of the layer. Originality/value The proposed approach allows for slice data representation for any material combination that can be defined mathematically. Three different material types, namely, composite material, functionally graded materials and combination thereof, are provided as examples. These data form the input data for subsequent tool path planning.

Correspondence Principle in Viscoelastic Functionally Graded Materials

2000 ◽  
Vol 68 (1) ◽  
pp. 129-132 ◽  
Author(s):  
G. H. Paulino ◽  
Z.-H. Jin
Keyword(s):  
Functionally Graded Materials ◽  
Correspondence Principle ◽  
Functionally Graded ◽  
Viscoelastic Materials ◽  
Viscoelastic Solids ◽  
Graded Materials ◽  
Space And Time ◽  
Separable Functions

This paper presents an extension of the correspondence principle (as applied to homogeneous viscoelastic solids) to nonhomogeneous viscoelastic solids under the assumption that the relaxation (or creep) moduli be separable functions in space and time. A few models for graded viscoelastic materials are presented and discussed. The revisited correspondence principle extends to specific instances of thermoviscoelasticity and fracture of functionally graded materials.

Creep Behavior of Pressurized Tank Composed of Functionally Graded Materials

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
JianJun Chen ◽  
KeeBong Yoon ◽  
Shan-Tung Tu
Keyword(s):  
Functionally Graded Materials ◽  
Stress Level ◽  
Creep Behavior ◽  
Creep Property ◽  
Closed Form Solution ◽  
Functionally Graded ◽  
Radial Coordinate ◽  
Time Step ◽  
Graded Materials ◽  
Creep Stress

The creep behavior of a pressurized tank, which is assumed to be made of functionally graded materials, is studied in this paper. The elastic response under the internal and external pressures is first obtained when Young’s modulus obeys a power function along with the wall thickness. If the creep exponent remains constant and the creep coefficient varies with the radial coordinate, a closed-form solution can be derived for the time-dependent behavior of the spherical tank. The effects of material gradients on the creep stress and strain are investigated in detail. The results show that the stress level under the steady creep state is determined by the distribution of the creep properties. However, the magnitude of the creep strain is influenced by the elastic modulus distribution, as well as the creep property distribution inside the functionally graded materials. Compared with the finite element analysis results, the optimum time step value is also investigated. Some fundamental knowledge of the materials distribution is achieved to reduce the maximum creep stress/strain and to uniformize the stress level inside the functionally graded materials tank.

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