  We propose an adaptive polygonal finite element formulation for collapse
plastic analysis of solids. The article contributes into four crucial points:
1) Wachspress shape functions at vertex and bubble nodes handled at a
primal-mesh level; 2) plastic strain rates and dissipation performed over a
dual-mesh level; 3) a new adaptive primal-mesh strategy driven by the L^2
-norm-based indicator of strain rates; and 4) a spatial decomposition structure
obtained from a so-called polytree mesh scheme. We investigate both purely
cohesive and cohesive-frictional materials. We prove numerically that the
present method performs well for volumetric locking problem. In addition, the
optimization formulation of limit analysis is written by the form of
second-order cone programming (SOCP) in order to exploit the high efficiency of
interior-point solvers. The present method retains a low number of optimization
variables. This convenient approach allows us to design and solve the
large-scale optimization problems effectively. Numerical validations show the
excellent performance of the proposed method.
