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For the first time, we have obtained accurate numerical solutions for
wave propagation in inhomogeneous materials under impact loading. We have
extended the earlier developed numerical approach for elastodynamics
problems in homogeneous materials to inhomogeneous materials. The approach
includes the two-stage time-integration technique with the quantification
and the filtering of spurious oscillations, the special design of
non-uniform meshes as well as includes the standard finite elements and the
elements with reduced dispersion. Similar to wave propagation in
homogeneous materials in the 1-D case, we have obtained very accurate
results for composite and functionally graded materials using the linear
elements with lumped mass matrix and the explicit central difference
method. We have also shown that specific non-uniform meshes yield much more
accurate results compared to uniform meshes. We have also shown the
efficiency of the finite elements with reduced dispersion compared with the
standard finite elements.
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