  In the standard SPH method, the interaction between two particles might be
not pairwise when the support domain varies, which can result in a reduction of
accuracy. To deal with this problem, a modified SPH approach is presented in
this paper. First of all, a Lagrangian kernel is introduced to eliminate
spurious distortions of the domain of material stability, and the gradient is
corrected by a linear transformation so that linear completeness is satisfied.
Then, concepts of support and dual-support are defined to deal with the
unbalanced interactions between the particles with different support domains.
Several benchmark problems in one, two and three dimensions are tested to
verify the accuracy of the modified SPH model and highlight its advantages over
the standard SPH method through comparisons.
