Upper bound adaptive finite element method with higher-order element based on Drucker-Prager yield criterion

An upper bound adaptive finite element method with six-node triangular high-order element, which is based on Drucker-Prager yield criterion, is established. Based on the upper bound theory, the corresponding calculation program is compiled. The element dissipative energy is used as the control index in the adaptive refine strategy. Based on the calculated results of element dissipative energy, the mesh is refined by dividing the element with high dissipative energy into two parts, and the upper bound finite element adaptive calculation is completed through repeated calculation based on the refined mesh. The influences of a series of Drucker-Prager yield criteria on the upper limit solution are analyzed depending on the calculated results of stability of tunnels and bearing capacity of strip footings. The calculated results also show that the proposed upper bound finite element method can achieve high accuracy, and the failure modes can be obtained by the mesh distribution.