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Mass moments of functionally graded 2D domains and axisymmetric solids
We present a general methodology to evaluate the mass moments of two-dimensional domains and axisymmetric solids made of functionally graded materials. The approach developed in the paper is based on the sequence of two steps. First, the original domain integrals are converted to integrals extended...
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Published in: | Applied mathematical modelling 2024-05, Vol.129, p.250-274 |
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Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites |
Online Access: | Get full text |
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Summary: | We present a general methodology to evaluate the mass moments of two-dimensional domains and axisymmetric solids made of functionally graded materials. The approach developed in the paper is based on the sequence of two steps. First, the original domain integrals are converted to integrals extended to the relevant boundary by exploiting Gauss theorem. Second, for domains having a polygonal or circular shape, the boundary integrals are evaluated analytically by providing algebraic expressions that depend upon the parameters defining the density distribution, the position vectors of the vertices of the polygonal domain or the initial and ending points of an arbitrary circular sector, respectively. While the first step refers to moments of arbitrary order, the second step is limited to the most useful quantities for engineering applications, i.e. generalised mass, static moment and inertia tensor. The formulas derived in the paper are validated by means of examples retrieved from the specialised literature for which analytical results are available or have been specifically derived by the authors. Finally, in order to ascertain the computational savings entailed by the use of the proposed analytical formulas with respect to numerical techniques, the mass moments of a longitudinal section of a human femure, made of a functionally graded material and characterised by a linear density distribution, have been computed.
•Mass moments for functionally graded domains expressed by boundary integrals.•Polynomial, exponential and polynomial quadratic density distributions.•General methodology for computing mass moments of order greater than 2.•Analytical evaluation of mass moments for polygonal or circular domains.•Accuracy and computational efficiency of the analytical formulas. |
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ISSN: | 0307-904X |
DOI: | 10.1016/j.apm.2024.01.028 |