The best grading pattern selection for the axisymmetric elastic response of pressurized inhomogeneous annular structures (sphere/cylinder/annulus) including rotation

Abstract

Many models were offered in the literature to simulate the material gradation patterns within the functionally graded metalceramic structures. The present study provides a comprehensive and comparative numerical examination of the displacement and stress distributions in the three types of annular structures, namely spheres, cylinders, and annuli by gathering most of models up. To this end, an efficacious and accurate numerical method, the complementary functions method, is exploited in the numerical determination of the elastic fields with several material-grading patterns under internal pressure including centrifugal forces to search the best one exhibiting desired elastic axisymmetric behavior of such structures. A functionally graded material, viz., a particle reinforced composite, is assumed to be composed of an aluminum oxide (ceramic/Al 2 O 3) and a stainless steel (metal/SUS-410). Different grading patterns are formed by using several material grading rules such as a simple power rule, an exponential rule, a linear function, a Voigt mixture with power of volume fractions of constituents, a Mori-Tanaka scheme, Chung and Chi's Sigmoid function, Chen and Lin's sine rule, Dryden and Jayaraman's combined power and exponential rule, and finally Tornabene's four-parameter symmetric/asymmetric power functions. Variation of the elastic fields is presented in both tabular and graphical forms. Combined effects of both the pressure and rotation are also studied for cylinders and annuli having aspect ratios of 0.6 and 0.9. It is observed in the chosen patterns that a pattern with gradually increasing ceramic constituents toward a full ceramic layer at the outer surface is found as the best under pressure loads. Combined pressure plus centrifugal forces require a pattern having a full ceramic layer at the inner surface following a decreasing pattern with ceramic constituent toward the outer surface. The results with plain stress assumption are found somewhat higher than the results with generalized plane strain. As expected, the spheres have significantly smallest elastic fields than the others under the same pressure loads and aspect ratios.

Numerical Elastic Analysis of Functionally Graded (FG) Polar Orthotropic and Exponentially Varying-Thickness Rotating Disks via Combined Complementary Functions and the Transfer Matrix Methods

“…For example, concentric disks may be studied by TMM without increasing the size of matrices and also considering the residual internal stresses at the intermediate contact surfaces of the disks. Due to these reasons, and to build a foundation for such kinds of advanced problems [77][78][79][80][81], the transfer matrix method solution technique in which the transfer matrix has been obtained with the help of CFM is preferred in this study.…”

Comprehensive elastic analysis of functionally graded variable thickness pressurized disk

“…Before getting into the numerical examples, we would like to exhibit the preciseness of the analytical model. For this reason, our results are compared with a related study [43]. In that reference, the author has taken the Young's modulus as $${\rm{E}}( {\rm{r}} ) = {{\rm{E}}_{\rm{o}}}\;( {{\rm{r}}/a} ){^{{\alpha}}}$$.…”

“…In ref. [43], the researcher has preferred the usual constant Poisson's approach ($${\rm{\beta \;}}$$= 0). In the verification procedure, if β is set to be zero, we obtain an identical analytical solution to the reference (Cauchy‐Euler type).…”

Assessment of a hydraulic bottle jack as an effective device for controlling vibration and mitigating the effects of earthquakes

“…This concept has found a wide range of applications in engineering problems, where a typically elastic behavior is an intrinsic part of the process. [22][23][24][25][26][27] In view of their properties, springs have been used as energy absorbers, to command and revert mechanical systems, interceptors of static and dynamic forces, to strengthen joints, as dampers in anti-vibration protection systems, and as devices for controlling and measuring force. 28 In mathematical terms, a system consisting of springs can be solved by numerical methods 29 or through the use of advanced analytical techniques.…”