The Material Point Method (MPM) performs well in simulating large deformations of continua, such as debris flows. However, when structural components are involved in simulations, the grid sizes of the simulated continua are often overly coarse relative to the structural elements, which increases the difficulty of accurately assessing
the internal stresses of the structural members. Thus, this study introduces beam-column elements into the MPM, leveraging beam theory to improve the accuracy of stress calculations. The beam-column elements and the MPM are
integrated using a two-stage contact algorithm. In the first stage, the beam-column elements are treated as velocity
boundary conditions in the MPM to obtain nodal boundary forces, and in the second stage, these forces are used to
update the states of both the beam-column elements and the MPM-simulated continua. Numerical experiments reveal
that although the proposed projection-point-searching algorithm is less efficient under large displacements, the use of beam-column elements can prevent shear locking and enhance the accuracy of the internal flexural stress field of the structural members in MPM simulations. Moreover, simulations involving beam-column elements are significantly
more efficient than particle-based simulations of structural members.
Key Words: Material point method, beam-column elements, contact algorithm, beam theory.