Mojtaba Sadighi

Experimental and Numerical Investigation of Metal Type and Thickness Effects on the Impact Resistance of Fiber Metal Laminates

The impact response of fiber metal laminates (FMLs), has been investigated with experiments and numerical simulations, which is reported in this article. Low-velocity impacts were carried out to study the effects of metal type and thickness within FMLs. Glare5-3/2 laminates with two aluminum layer thicknesses and a similar FML containing magnesium sheets were impacted by drop weight tests. Also, a major part of this study was to accomplish a dynamic non-linear transient analysis to study the impact response of FMLs using the commercial finite element (FE) analysis code ABAQUS. By reviewing different approaches of modeling constituents of an FML, it is shown that the appropriate selection of elements has more significant role than failure criterion to predict acceptable results for this type of laminate and loading. The good agreement obtained between experimental and numerical results verifies the possibility of relatively simpler simulation by FE-analysis to predict overall response of FMLs under impact loading.

Static, Dynamic and Free Vibration Analysis of Functionally Graded Piezoelectric Panels Using Finite element method

In this article, analysis of the static bending, free vibration, and dynamic response of functionally graded piezoelectric panels have been carried out by finite element method under different sets of mechanical, thermal, and electrical loadings. The temperature field is assumed to be of uniform distribution over the panel surface and through the thickness of panel. The governing equations are obtained using potential energy and Hamilton’s principle based on the first-order shear deformation theory that includes thermo-piezoelectric effects. The finite element model is derived on the basis of constitutive equation of piezoelectric material accounting for coupling between elasticity and electric effect by four node elements. The present finite element is modeled with displacement components and electric potential as nodal degrees of freedom. The temperature field is calculated by post-computation through constitutive equation. Results are presented for two constituent FGPM panels under different mechanical boundary conditions. Numerical results for PZT-4/PZT-5H panels are given in both dimensionless tabular and graphical forms. Effects of material composition and boundary conditions on static bending, free vibration, and dynamic response are also studied. The numerical results obtained by the present model are in good agreement with the available solutions reported in the literature.

Mechanics of additively manufactured porous biomaterials based on the rhombicuboctahedron unit cell

Thanks to recent developments in additive manufacturing techniques, it is now possible to fabricate porous biomaterials with arbitrarily complex micro-architectures. Micro-architectures of such biomaterials determine their physical and biological properties, meaning that one could potentially improve the performance of such biomaterials through rational design of micro-architecture. The relationship between the micro-architecture of porous biomaterials and their physical and biological properties has therefore received increasing attention recently. In this paper, we studied the mechanical properties of porous biomaterials made from a relatively unexplored unit cell, namely rhombicuboctahedron. We derived analytical relationships that relate the micro-architecture of such porous biomaterials, i.e. the dimensions of the rhombicuboctahedron unit cell, to their elastic modulus, Poissons ratio, and yield stress. Finite element models were also developed to validate the analytical solutions. Analytical and numerical results were compared with experimental data from one of our recent studies. It was found that analytical solutions and numerical results show a very good agreement particularly for smaller values of apparent density. The elastic moduli predicted by analytical and numerical models were in very good agreement with experimental observations too. While in excellent agreement with each other, analytical and numerical models somewhat over-predicted the yield stress of the porous structures as compared to experimental data. As the ratio of the vertical struts to the inclined struts, α, approaches zero and infinity, the rhombicuboctahedron unit cell respectively approaches the octahedron (or truncated cube) and cube unit cells. For those limits, the analytical solutions presented here were found to approach the analytic solutions obtained for the octahedron, truncated cube, and cube unit cells, meaning that the presented solutions are generalizations of the analytical solutions obtained for several other types of porous biomaterials.

Mechanical properties of regular porous biomaterials made from truncated cube repeating unit cells: Analytical solutions and computational models

Additive manufacturing (AM) has enabled fabrication of open-cell porous biomaterials based on repeating unit cells. The micro-architecture of the porous biomaterials and, thus, their physical properties could then be precisely controlled. Due to their many favorable properties, porous biomaterials manufactured using AM are considered as promising candidates for bone substitution as well as for several other applications in orthopedic surgery. The mechanical properties of such porous structures including static and fatigue properties are shown to be strongly dependent on the type of the repeating unit cell based on which the porous biomaterial is built. In this paper, we study the mechanical properties of porous biomaterials made from a relatively new unit cell, namely truncated cube. We present analytical solutions that relate the dimensions of the repeating unit cell to the elastic modulus, Poissons ratio, yield stress, and buckling load of those porous structures. We also performed finite element modeling to predict the mechanical properties of the porous structures. The analytical solution and computational results were found to be in agreement with each other. The mechanical properties estimated using both the analytical and computational techniques were somewhat higher than the experimental data reported in one of our recent studies on selective laser melted Ti-6Al-4V porous biomaterials. In addition to porosity, the elastic modulus and Poissons ratio of the porous structures were found to be strongly dependent on the ratio of the length of the inclined struts to that of the uninclined (i.e. vertical or horizontal) struts, α, in the truncated cube unit cell. The geometry of the truncated cube unit cell approaches the octahedral and cube unit cells when α respectively approaches zero and infinity. Consistent with those geometrical observations, the analytical solutions presented in this study approached those of the octahedral and cube unit cells when α approached respectively 0 and infinity.

Quasi-Static and Low-Velocity Impact Response of Fully Backed or Simply Supported Sandwich Beams

The present paper describes analysis of low-velocity transverse impact on sandwich beam, with composite faces from Eglass/epoxy and cores from Polyurethane or PVC. Boundary conditions are fully backed rigid or simply supported. This research is based on a step by step study to generate more reliable impact results. Indentation of laminated beam, indentation of sandwich beams, and three-point loading have been analyzed with existing theories and modeled with the FE code ABAQUS, also their results are compared with experimental results. In quasi-static three-point bending, energy is consumed through three mechanisms: indentation of laminated beam, indentation of sandwich beam, and bending of sandwich beam. Impact on fully backed specimen is modeled in two cases of impactor energies using mass spring model of SDOF (single-degree-of-freedom) and indentation stiffness, lower energy of impactor for elastic indentation of sandwich beams, and higher energy for indentation in plastic area. TDOF (two-degree-of-freedom) with flexural and contact stiffnesses are used for impact on simply supported beams. Impacts are simulated by ABAQUS, as well. Results can describe response of beam and impactor displacements in terms of core and faces thicknesses, core material, and impactor energies for static and impact results. The experimental results are in good agreement with the analytical and FE analyses.

Mechanical behaviour of functionally graded plates under static and dynamic loading

This article presents an analytical solution for the mechanical behaviour of rectangular plates made of functionally graded materials (FGMs) based on the first-order shear deformation theory (FSDT) and the third-order shear deformation theory (TSDT). The FGM plate is assumed to be graded across the thickness. The material properties of the FGM plate are assumed to vary continuously through the thickness of the plate according to a power law distribution of the volume fraction of the constituent materials, except Poissons ratio, which is assumed to be constant. The plate is subjected to a lateral mechanical load on its upper surface. The equations of motion are written based on displacement fields. The partial differential equations have been solved by the Fourier series expansion. Using the Laplace transform, unknown variables are obtained in the Laplace domain. The resulting formulations enable one to perform the static, dynamic, and free vibration analysis for both FSDT and TSDT plates. Employing the analytical Laplace inversion method and numerical time integration technique based on the Newmark method, time function solution of the problem is obtained and the unknown parameters are derived for a dynamic loading situation. Finally, the natural frequencies of the plate are obtained and dynamic responses are presented in the form of combinations of different frequencies. The results are verified with those reported in the literature.

Mechanical Properties of Additively Manufactured Thick Honeycombs

Honeycombs resemble the structure of a number of natural and biological materials such as cancellous bone, wood, and cork. Thick honeycomb could be also used for energy absorption applications. Moreover, studying the mechanical behavior of honeycombs under in-plane loading could help understanding the mechanical behavior of more complex 3D tessellated structures such as porous biomaterials. In this paper, we study the mechanical behavior of thick honeycombs made using additive manufacturing techniques that allow for fabrication of honeycombs with arbitrary and precisely controlled thickness. Thick honeycombs with different wall thicknesses were produced from polylactic acid (PLA) using fused deposition modelling, i.e., an additive manufacturing technique. The samples were mechanically tested in-plane under compression to determine their mechanical properties. We also obtained exact analytical solutions for the stiffness matrix of thick hexagonal honeycombs using both Euler-Bernoulli and Timoshenko beam theories. The stiffness matrix was then used to derive analytical relationships that describe the elastic modulus, yield stress, and Poisson’s ratio of thick honeycombs. Finite element models were also built for computational analysis of the mechanical behavior of thick honeycombs under compression. The mechanical properties obtained using our analytical relationships were compared with experimental observations and computational results as well as with analytical solutions available in the literature. It was found that the analytical solutions presented here are in good agreement with experimental and computational results even for very thick honeycombs, whereas the analytical solutions available in the literature show a large deviation from experimental observation, computational results, and our analytical solutions.

DYNAMIC AND STATIC ANALYSIS OF FGM SKEW PLATES WITH 3D ELASTICITY BASED GRADED FINITE ELEMENT MODELING

The present article deals with static and dynamic behavior of functionally graded skew plates based on the three-dimensional theory of elasticity. On the basis of the principle of minimum potential energy and the Rayleigh Ritz method, the equations of motion are derived in conjunction with the graded finite element approach. Solution of the resulted system of equations in time domain is carried out via Newmarks time integration method. Calculations are applied for fully clamped boundary condition. In the present paper, two different sets of distributions for material properties are considered. For the static analysis, material properties are considered to vary through the thickness direction according to an exponential law. In the case of dynamic analysis, variations of the volume fractions through the thickness are assumed to obey a power law function. Thus, the effective material properties at each point are determined by the Mori-Tanaka scheme. In case of dynamic analysis, the results are obtained for uniform step loadings. The effects of material gradient index and skew angle on displacement components and stress response are studied. Results of present formulations are verified by available results of a functionally graded rectangular plate for different boundary conditions and also compared with result of a homogenous skew plate by commercial FEM software.

Vibration and damping analysis of cylindrical sandwich panels containing a viscoelastic flexible core

In the present study, vibration and damping analysis of cylindrical sandwich panels containing a viscoelastic flexible core based on the high-order theory of sandwich structures is investigated. A layerwise formulation is developed to study the applicability of the high-order theory. The face sheets are considered as composite laminates with cross-ply layup that follow first-order shear deformation assumption and the core is considered as a linear viscoelastic medium with out-of-plane stresses only. The field equations along with the boundary conditions are derived via the application of Hamilton’s principle. A closed-form solution is developed for simply supported boundary conditions and a comparison is made with available results in the literature to verify the high-order and layerwise solution results. Finally, the influence of parameters including the core stiffness, the core to the face sheets thickness ratio, and the core damping on the applicability of the high-order theory, and variation of natural frequencies and modal loss factors of the sandwich panel are investigated. The results demonstrate a good agreement between the high-order and layerwise theories for small core stiffnesses, and for a wide range of the core to the face sheet thickness ratio and core damping.

Static Analysis of Cylindrical Sandwich Panels with a Flexible Core and Laminated Composite Face Sheets

In this study, static response of cylindrical sandwich panels with flexible core based on the high-order theory (HOT) of sandwich structures is investigated. A layerwise formulation is developed to study the applicability of HOT. The face sheets are considered as composite laminates with cross-ply layup that follow first-order shear deformation assumption and the core is considered as a linear elastic medium with out-of-plane stresses only. The field equations along with the boundary conditions are derived by means of the principle of minimum potential energy. A closed-form solution is developed for simply supported boundary conditions and a comparison is made with results from the commercial finite element software ANSYS to verify high-order and layerwise solution results. Finally, influence of parameters including the core to face sheets stiffness ratio and the core to face sheets thickness ratio on the applicability of HOT is investigated. Results demonstrate a good agreement between high-order and layerwise results for the small thickness ratio of the core to the face sheet and low stiffness cores.