Plastic strain was determined at multiple time increments.The strain was caused by stress and temperature.The yield function in high-temperature states is the function of temperature and plastic strain.The calculation efficiency would be decreased and much more calculation would be needed if a conventional method

such as the radial return method

was used.In the case of axial stress states

the temperature path was difficult to determine at various time intervals.Initial value equations were obtained with the Drucker-Prager function of plane stress concrete.This method can solve the previously mentioned problems efficiently when used with the Runge-Kutta integration strategy.A program was developed with an updated co-varying coordinate finite element method based on the S-R decomposition theorem.Computational results show that the integration strategy is highly accurate and efficient.