Analitical Solutions of Anisotropic Body Bounded by an Elleptical Surface Subjected to Arbitrary Loads

In this paper, the solution for the hollow cylindroid is analytically derived under two assumptions that (1) the cylindroid is consist of various anisotropic elastic material and (2) only both sides of the hollow cylindroid are subjected to arbitrary load, which will be expanded to complex form of Fourier series with period 2. To simplify an analysis, mapping function, which is mapped elliptical boundaries of the cylindroid to unit circle, and complex stress functions proposed by S. G. Lekhnitskii are introduced. These stress functions have undetermined coefficients, however, these coefficients can be determined by taking into account the boundary conditions for resultant stresses at both sides of the hollow cylindroid. In particular, undetermined coefficients in stress functions will be determined by comparing with complex Fourier coefficients for those resultant stresses. In the case of isotropic cylindroid, analytical solution for similar problem was already derived, however, there is one limit of application. This limit is related to the cross-sectional shape of hollow cylindroid. That is, if both sides of the hollow cylindroid did not have a same focus of an ellipse, analytical solution for isotropic case was not able to derive. On the other hand, the solution derived from this study does not have such a limit. So some numerical examples are shown by some figures and tables not only anisotropic case but also isotropic case.

show abstract

Analysis for an anisotropic hollow cylindroid subjected to arbitrary loadings

Tane

Sasaki

Tabuchi

et al. 2016

Transactions of the JSME (In Japanese)

View full text Add to dashboard Cite

show abstract

Analysis of piezoelectric materials and anisotropic materials subjected to arbitrary loads at the boundary (Similar formulation in elliptical plate problem and elliptical cavity problem)

Sasaki

Tane

Kabeyasawa

2014

Transactions of the JSME (In Japanese)

View full text Add to dashboard Cite

This paper presents general solutions for piezoelectric materials and anisotropic materials subjected to arbitrary loads at the boundary. General solutions are provided by using complex functions based on Lekhnitskii formalism. In the analysis, similarities of fundamental equation between piezoelectric materials and anisotropic materials are shown. By defining new similarity-based complex functions, expressions of mechanical and electrical quantities are derived by analogous form. It is shown that expression forms of electric displacement in piezoelectric materials are corresponding to those of out-of-plane share stress in anisotropic materials. And stress distribution, electric displacement distribution and coupling effect are shown by graphical representation from several analysis results.

show abstract

Similar Analysis of Piezoelectric Materials and Anisotropic Materials with Elliptical Cavity Subjected to Uniform Loads at Infinity

Sasaki

Tane

Kabeyasawa

2015

J. Soc. Mat. Sci., Japan

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Analitical Solutions of Anisotropic Body Bounded by an Elleptical Surface Subjected to Arbitrary Loads

Cited by 3 publications

References 4 publications

Analysis for an anisotropic hollow cylindroid subjected to arbitrary loadings

Analysis for an anisotropic hollow cylindroid subjected to arbitrary loadings

Analysis of piezoelectric materials and anisotropic materials subjected to arbitrary loads at the boundary (Similar formulation in elliptical plate problem and elliptical cavity problem)

Similar Analysis of Piezoelectric Materials and Anisotropic Materials with Elliptical Cavity Subjected to Uniform Loads at Infinity

Contact Info

Product

Resources

About