Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix d...Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix doesn’t exist or isn’t stable, the precision and stability of the algorithms will be afected. An explicit series solution of the state equation has been pre- sented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented. The algorithm is more precise and stable than the explicit series solution and isn’t sensitive to the time-step. Finally, a numerical example is presented to demonstrate the efectiveness of the algorithm.展开更多
One developing commercial vehicle was simulated on crashworthiness using the nonlinear finite element method. The deformation of the auto-body, the movement of the steering wheel and the dynamic responses of the occup...One developing commercial vehicle was simulated on crashworthiness using the nonlinear finite element method. The deformation of the auto-body, the movement of the steering wheel and the dynamic responses of the occupant at the initial velocity of 50 km/h were studied. The results show that the design of the vehicle could be improved on structure and material. The frontal longitudinal beam, the main energy-absorbing part of the auto-body, was optimized on structure. The data of the simulation predict that the hinge of the engine hood would fracture during the crash. The failure of the engine hood hinge would be a danger to both the driver and passengers. Then the problem was solved by changing the engine hood and hinge on structure and material. Simulation results also show that applying new material and new manufacture techniques could improve the crashworthiness of the vehicle greatly. These improvement methods are valuable to the virtual design of vehicles.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.60273048and60174023).
文摘Nonlinear dynamic equations can be solved accurately using a precise integration method. Some algorithms exist, but the inversion of a matrix must be calculated for these al- gorithms. If the inversion of the matrix doesn’t exist or isn’t stable, the precision and stability of the algorithms will be afected. An explicit series solution of the state equation has been pre- sented. The solution avoids calculating the inversion of a matrix and its precision can be easily controlled. In this paper, an implicit series solution of nonlinear dynamic equations is presented. The algorithm is more precise and stable than the explicit series solution and isn’t sensitive to the time-step. Finally, a numerical example is presented to demonstrate the efectiveness of the algorithm.
文摘One developing commercial vehicle was simulated on crashworthiness using the nonlinear finite element method. The deformation of the auto-body, the movement of the steering wheel and the dynamic responses of the occupant at the initial velocity of 50 km/h were studied. The results show that the design of the vehicle could be improved on structure and material. The frontal longitudinal beam, the main energy-absorbing part of the auto-body, was optimized on structure. The data of the simulation predict that the hinge of the engine hood would fracture during the crash. The failure of the engine hood hinge would be a danger to both the driver and passengers. Then the problem was solved by changing the engine hood and hinge on structure and material. Simulation results also show that applying new material and new manufacture techniques could improve the crashworthiness of the vehicle greatly. These improvement methods are valuable to the virtual design of vehicles.
