Effects Of Material Distribution Research Articles

Non-linear behavior of functionally graded elastoplastic beam under torsion

The torsional behavior of beams graded in one and two directions under large displacements and angular deformations was analyzed using the power law and sinusoidal functions. Functionally graded material is elastoplastic, consisting of ceramic and metal. A nonlinear finite element method with isoparametric hexahedral elements was used. The finite element formulation was made using the updated Lagrangian formulation based on the virtual displacement principle. An iterative solution using Newton-Raphson and updated Newton-Raphson methods was used to solve the nonlinear equation system. The propagation of the plastic zone was calculated based on the flow theory of plasticity. Elastoplastic behavior and effective material properties were determined according to the TTO model. Numerical investigations have shown that functionally graded beams behave quite differently from homogeneous beams under torsion. Yielding of the material starts at the outer boundaries of the section of the homogeneous beams, and the plastic zone propagates symmetrically. On the other hand, yielding and propagation of plastic zones tend to shift to regions with more ceramic volume with higher effective Young modulus in functionally graded beams. Unlike homogeneous beams, the largest shear stresses can occur within the section rather than at the outer boundaries of the section. In beams graded from ceramic to metal using the power law, the section moves along the transverse direction in addition to the rotation. This transverse displacement occurs in the grading direction, and its magnitude is about 3% of the thickness at 12.5° rotation angle. Also, the shear stresses are not zero in the section's midpoint. The effects of material distribution on displacements, stresses, and plastic zone propagation were examined, and essential points were reported.

Size-dependent behaviours of functionally graded sandwich thin-walled beams based on the modified couple stress theory

This paper examines the static and vibration analysis of functionally graded sandwich thin-walled microbeams using the modified couple stress theory. The material properties in both web and flanges vary continuously through their thickness. The equations of motion are derived and solved by the Ritz method. Verification studies are performed on the bending and vibration responses of FG sandwich thin-walled beams. The effects of material distribution, span-to-height's ratio, and material length scale parameters on the responses of microbeams for various boundary conditions are investigated. The results of the analysis indicate that the deflections and natural frequencies of functionally graded sandwich thin-walled microbeams are greatly influenced by the variations of parameters mentioned earlier. The microbeams with the size effect are predicted to be much stiffer than their macro counterparts. Some benchmark results can be used as a reference for future studies.

SIMPLE INCREMENTAL APPROACH FOR ANALYSING OPTIMAL NON-PRISMATIC FUNCTIONALLY GRADED BEAMS

This paper presents a simple incremental approach of analysing the static behaviour of functionally graded tapered beams. This approach involves dividing the non-uniform beam into segments with uniform cross-sections, and using two separate finite element models to analyse the structural behavior of slender beams (Euler-Bernoulli model) and deep beams (Timoshenko beam theory). The material properties of the beam vary according to a power law distribution through the thickness, resulting in smooth variations in the mechanical properties. The finite element system of equations is obtained using the principle of virtual work. Detailed information on the shape functions and stiffness matrix of the beam is provided, and the numerical results are evaluated and validated using data from the literature. The comparison demonstrates that the response of the functionally graded tapered beams is accurately assessed by the proposed approach. Additionally, the effects of material distribution, boundary conditions, and tapering parameter on the deflection behavior are presented. Results show that an increase in the power law index increases the flexibility of the functionally graded tapered beams, resulting in higher deflection. Furthermore, lower tapering parameters also result in higher deflection. Compared to other boundary conditions, clamped-clamped boundary conditions demonstrate the best performance in terms of maximum deflection.

Natural Frequencies of a Viscoelastic Supported Axially Functionally Graded Bar With Tip Masses

The frequency parameters of an Axially Functionally Graded (AFG) bar for viscoelastic and point mass boundary conditions are studied in this paper. The structures with functionally graded materials under axial loads can be modelled as AFG bars. Those may be considered as support elements with spring and dashpot in the vibration isolation. Keeping the ratio of force frequency and natural frequency at a certain level is ensured to control the natural frequency therefore dynamic amplification factor with different material combinations. Various boundary conditions are attained by changing the spring and damping coefficients of viscoelastic support elements and the ratio of rod mass to tip mass. Researchers assume that the beam material properties in directions of length and thickness change exponentially, individually, or both in their studies. There are a few studies on the AFG rods in the existing studies. Analysis is carried out via the finite element method for the non-dimensional frequency parameters of the bar in MATLAB. The energy equations of the motion are obtained in the frame of axial bar theory considering the material properties of the bar vary longitudinally according to the power-law distribution. The effects of material distribution, spring, damping and tip mass values on the bar's frequency parameters and structural behaviour have been extensively investigated.

Effect of material distribution on bending and buckling response of a bidirectional FG beam exposed to a combined transverses and variable axially loads

This article considers a bidirectional functionally graded (BDFG) beam with various distributions of volume fraction. The impact of these distributions on the buckling and bending response of BDFG beam with general boundary conditions is investigated via a quasi-3D solution. It is assumed that the beam is exposed to a set of in-plane varying compressive loads and there mechanical characteristics change in both directions. Also, the BDFG beam is considered to be exposed different external mechanical loads. Hamilton’s principle is employed to derive the governing equations, which are then solved using analytical solution to obtain buckling and bending characteristics. The precision of the current formulation is investigated via a comparison with available data in literature. Some numerical results are presented and discussed to assess the effect of different parameters such type of volume fraction, boundary condition, varying load, and beam geometry on the buckling and bending of BDFG beam.

The effect of material distribution on the out-of-plane elastic properties of hierarchical diamond honeycombs

Inspired by the natural honeycomb structure, a novel bio-inspired hierarchical diamond honeycomb with variable wall thickness (HDH-VT) is proposed by introducing a bio-inspired material distribution design into hierarchical diamond honeycomb (HDH) in this study. A full-scale finite element technique is proposed to simulate the compression and transverse shear tests and employed to numerically calculate the out-of-plane elastic properties of HDH and HDH-VT. Theoretical models for the out-of-plane Young’s and shear moduli of HDH and HDH-VT are developed and validated. The effects of geometric parameters and relative density on the Young’s and shear moduli of HDH and HDH-VT are analyzed. The results indicate that the elastic properties of HDH and Young’s modulus of HDH-VT are only related to the relative density. In addition, the out-of-plane shear modulus of HDH-VT is significantly affected by the material distribution. The shear modulus of HDH-VT can be widely tailored by adjusting geometric parameters without sacrificing Young’s modulus. This study provides a novel strategy for the design of the skin material of morphing aircraft with widely tailorable mechanical properties.

Novel periodic pile barriers in saturated soil and applications to propagation attenuation of shear plane waves

The frequency attenuation zones (AZs) of periodic pile barriers have attracted extensive attention in recent years due to their superior performance in ambient vibration reduction. However, the research on vibration isolation of pile barriers in saturated soil is very limited. Also, the configuration of the traditional pile barrier is simple and the AZ width is narrow, which limits its application in engineering practice. In this paper, to develop novel periodic pile barriers with the maximum relative attenuation zone width (RWAZ) in saturated soil, the topology optimization on the periodic pile unit is carried out with the genetic algorithm (GA) and FEM. For different site conditions, the effects of the saturated soil porosity, the drained elastic modulus, the drained density and the tortuosity coefficient of soil on the optimization results are analyzed, and the corresponding optimized pile structures are proposed, respectively. Thus, the effect of material distribution on the RWAZ is disclosed, and novel periodic pile structures for ambient vibration isolation in saturated soil are developed. Furthermore, the superior shear plane wave attenuation performances of the optimized pile structure in saturated soil are both demonstrated by the established 2D and 3D numerical models.

The Effects of Material Distribution and Flow Profile on the Stability of Cantilevered Axially Functionally Graded Pipes

Abstract This article investigates the influences of different material distribution types and flow profiles in the cross section on dynamics of cantilevered axially functionally graded (AFG) pipe. Functionally graded material as a designable material, its appliance in structures can enhance the stability of the structure by adequately choosing the material constituents and arranging constituents' distribution. The governing equation of the pipe system is derived based on the Euler–Bernoulli beam theory and numerically solved by the differential quadrature method (DQM). The influences of different volume fraction function and nonuniform flow velocity distribution on the natural frequencies and average critical flow velocities are discussed according to the numerical results. It can be concluded that the enhanced effect of the AFG material is mainly caused by an increment in the amount of stiffer constituent. With the same amount, pure distribution difference in exponential or power function type that brings stiffer fixed end results in slightly higher critical velocity against flutter. Ignoring the nonuniform flow velocity distribution leads to an overestimation of the pipe's stability and the overestimation is even apparent on AFG pipe. Nonuniform velocity distribution affects the stable flow velocity area and appearance of restabilizing phenomena.

Effects of nonlinear hygro-thermo-mechanical loading on the bending response of nanobeams using nonlocal strain gradient theory

This article analyzes the bending response of functionally graded nanobeams under hygro-thermo-mechanical loadings. The nonlocal strain gradient theory (NSGT) is implemented to consider both hardening and softening impacts on the system response. The nanobeam is constructed of functionally graded materials (FGMs), whose characteristics change smoothly across the thickness direction according to a power-law distribution function. The system is subjected to hygro-thermal environments according to the sinusoidally distributed loading. By employing Hamilton's principle, the static equations of the system are acquired. Static responses of the nanobeam are obtained with the help of the Galerkin technique. The effects of material distribution and different boundary conditions on the system deflection are examined. The impacts of several system parameters, such as the nonlocal parameter, length scale parameter, temperature gradient, and moisture variation, on the static responses of the functionally graded nanoscale beams are determined.

An improved shear deformable theory for bending and buckling response of thin-walled FG sandwich I-beams resting on the elastic foundation

This paper proposes an improved first-order beam theory by separation of variables for bending and buckling analysis of thin-walled functionally graded (FG) sandwich I-beams resting on a two-parameter elastic foundation. By dividing the displacements into bending and shear parts, this model can produce the deflections for both two cases with and without shear effect. The mechanical properties of beams based on the power law distribution of volume fraction of ceramic or metal. Governing equations are established from Lagrange’s equations. The new Ritz’s approximation functions, which are combined between orthogonal polynomial and exponential functions, are proposed to solve problem. The deflections and critical buckling loads of thin-walled FG sandwich I-beams are presented and compared with those available literature to verify the present theory. The effects of material distribution, boundary conditions, length-to-height ratio, shear deformation and foundation parameters on the results are investigated in detail.

Structural Analysis and Size Optimization of a Fine-Blanking Press Frame Based on Sensitivity Analysis

The fine-blanking press, which has been widely used in the sheet-cutting industry, is high-end equipment. The frame is a core component of the fine-blanking press. In this paper, the sensitivity analysis and size optimization method were used to optimize a fine-blanking press frame. First, a shell element model of the frame was established to analyse the mechanical properties of the initial frame. Then, the mathematical expressions for sensitivity analysis and size optimization of the frame were formulated. Based on the established model, the response sensitivities for plate thicknesses were analysed, and a 12.94 % weight reduction was achieved through size optimization. Moreover, the effect of material distribution on dynamic performance was investigated. The result indicated that for a constrained structure, distributing material close to the constraint location increases the modal frequencies.

STATIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED SANDWICH PLATES USING A THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT MODEL

In this paper, static bending of two-direction functionally graded sandwich (2D-FGSW) plates is studied by using a finite element model. The plates consist of a homogeneous core and two functionally graded skin layers with material properties being graded in both the thickness and length directions by power gradation laws. Based on a third-order shear deformation theory, a finite element model is derived and employed in the analysis. Bending characteristics, including deflections and stresses are evaluated for the plates with classical boundary conditions under various types of distributed load. The effects of material distribution and layer thickness ratio on the static bending behavior of the plates are examined and highlighted.

STATIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED SANDWICH PLATES USING A THIRD-ORDER SHEAR DEFORMATION FINITE ELEMENT MODEL

In this paper, static bending of two-direction functionally graded sandwich (2D-FGSW) plates is studied by using a finite element model. The plates consist of a homogeneous core and two functionally graded skin layers with material properties being graded in both the thickness and length directions by power gradation laws. Based on a third-order shear deformation theory, a finite element model is derived and employed in the analysis. Bending characteristics, including deflections and stresses are evaluated for the plates with classical boundary conditions under various types of distributed load. The effects of material distribution and layer thickness ratio on the static bending behavior of the plates are examined and highlighted.

Research on Two-stage Multi-objective Integer Programming Model of Helicopter Distribution Materials in Emergency Logistics

Based on the earthquake disaster, this paper introduces the JIT just-in-time thinking of logistics management, and builds a three-level supply chain network consisting of helicopters, warehouses and material demanders. On this basis, aiming at maximizing the seismic performance, radiation range and optimal helicopter dispatching plan of the material reserve, and establishing the warehouse location and material distribution as the decision variables, a two-stage multi-objective integer programming model is established. The feasibility and effectiveness of the model are verified by specific case analysis, and the efficiency and effect of material distribution in the earthquake disaster reduction system are improved. In addition, according to the actual earthquake disaster area, the model was improved by the ant colony optimization algorithm.

Cell- and Node-Based Smoothing MITC3-Finite Elements for Static and Free Vibration Analysis of Laminated Composite and Functionally Graded Plates

Cell- and node-based smoothing MITC3-finite elements for static and free vibration analysis of laminated composite and functionally graded plates are proposed in this paper. It is based on a higher-order shear deformation theory which accounts for a higher-order variation of in-plane displacements and traction-free boundary conditions on top and bottom surfaces of transverse shear stresses. Novel CS-MITC3 and NS-MITC3 finite elements are proposed in which an MITC3 three-node triangle element with seven degrees-of-freedom per nodes that only requires the [Formula: see text]-type continuity is developed, and then cell- and node-based smoothing techniques are applied. Numerical results for the laminated composite and functionally graded plates are proposed to validate the accuracy of developed theory and to investigate the effects of material distribution and side-to-thickness ratio on the deflection, stresses and natural frequencies of the plates.

Hygro-Thermal Nonlinear Analysis of a Functionally Graded Beam

Nonlinear behavior of a functionally graded cantilever beam is analyzed under non-uniform hygro-thermal effect. To solve this problem, finite element method is applied within plane solid continua. Total Lagrangian approach is utilized in the nonlinear kinematic relations. Newton-Raphson method with incremental displacement is used in nonlinear solution. Comparison study is performed. Effects of material distribution, temperature and moisture changes on nonlinear deflections of the functionally graded beam are presented and discussed.

Geometrically nonlinear analysis of functionally graded porous beams

In this paper, geometrically non-linear analysis of a functionally graded simple supported beam is investigated with porosity effect. The material properties of the beam are assumed to vary though height direction according to a prescribed power-law distributions with different porosity models. In the nonlinear kinematic model of the beam, the total Lagrangian approach is used within Timoshenko beam theory. In the solution of the nonlinear problem, the finite element method is used in conjunction with the Newton-Raphson method. In the study, the effects of material distribution such as power-law exponents, porosity coefficients, nonlinear effects on the static behavior of functionally graded beams are examined and discussed with porosity effects. The difference between the geometrically linear and nonlinear analysis of functionally graded porous beam is investigated in detail. Also, the effects of the different porosity models on the functionally graded beams are investigated both linear and nonlinear cases.

State-space Levy solution for size-dependent static, free vibration and buckling behaviours of functionally graded sandwich plates

The size-dependent static, free vibration and buckling behaviours of functionally graded (FG) sandwich plates are analysed in this study. Utilising the modified couple stress theory and variational principle, governing equations of motion are developed with a refined shear deformation theory. The rectangular plates embedded on two opposite simply-supported edges with the arbitrary combinations of the other two. Based on the state-space Levy solution, the deflections, stresses, natural frequencies and critical buckling loads are analytically solved for the closed-form formulations. The effects of material distribution and graded schemes, geometric parameters and boundary conditions are also investigated to examine the size-dependent behaviours of FG sandwich microplates.

Dynamic analysis and wave propagation in rotating heterogeneous cylinders under moving load and thermal conditions; implementing an efficient mesh free method

In this paper, dynamic analysis of thick hollow rotating cylinder with finite length made of two-dimensional functionally graded material subjected to a moving mechanical load is investigated. Before applying of any mechanical load, the cylinder is under initial stresses due to initial steady state temperature gradient and rotational velocity. Then a moving mechanical distributed load excites the inner boundary surface of the cylinder. Meshless local Petrov–Galerkin (MLPG) method has been rearranged and implemented in order to discretize the governing equations in the spatial domain. The resulting sets of differential equations are then solved by Newmark time integration scheme in the temporal domain. The time histories of displacements and stresses components as well as 2D stress wave propagation are obtained for various scheme of volume fraction distribution. By implementing the presented meshless technique, the effects of material distribution, moving load, rotational body forces and thermal loading on the dynamic behavior of the FG cylinder have been investigated. The achieved results show that the effects of temperature on the stresses are greater and more important than the internal moving pressure or body force due to rotational speed. The MLPG method introduces itself as a very effective method with high accuracy for stress wave propagation and dynamic analysis of 2D-FGMs.

Nonlinear static analysis of functionally graded porous beams under thermal effect

This paper deals with the nonlinear static deflections of functionally graded (FG) porous under thermal effect. Material properties vary in both position-dependent and temperature-dependent. The considered nonlinear problem is solved by using Total Lagrangian finite element method within two-dimensional (2-D) continuum model in the Newton-Raphson iteration method. In numerical examples, the effects of material distribution, porosity parameters, temperature rising on the nonlinear large deflections of FG beams are presented and discussed with porosity effects. Also, the effects of the different porosity models on the FG beams are investigated in temperature rising.