Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Paradoxes of differential nonlocal cantilever beams: Reasons and a novel
  solution   The paradoxes of differential nonlocal models have been attributed to the
inconsistency in forming the nonlocal boundary conditions. To overcome these
paradoxes, nonlocal boundary conditions should be correctly formed. However,
still forming these boundary conditions for differential nonlocal models is a
challenging task. To resolve the trouble, in this study, the iterative nonlocal
residual approach is employed. In the context of this approach, the field
equation is solved in the local field with an imposed nonlocal residuals. This
nonlocal residual is iteratively formed (not determined) depending on a
pre-determined local field. The iterative nonlocal residual approach permits
applying the local boundary conditions. Thus, the paradoxes of differential
nonlocal models due to the nonlocal boundary conditions are effectively solved.
The paradoxes of differential nonlocal models and reasons behind them are
discussed. Moreover, a nonlocal beam model based on the iterative nonlocal
residual approach is proposed. This nonlocal beam model is employed to
investigate the static bending and free vibration of differential nonlocal
cantilever beams. Comparisons between the results of the iterative nonlocal
residual approach and results of integral nonlocal beam models are carried out.
It is demonstrated that the iterative nonlocal residual approach gives the same
results as integral nonlocal models.

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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ