A unified approach to three finite element theories for geometric nonlinearity

Abstract The paper considers theoretical and numerical questions associated with finite element analysis of geometrically nonlinear structural problems. A variety of finite element theories have recently arisen leading to geometric stiffness matrices, initial displacement matrices, and other similar forms. The present analysis determines an integrated unified approach to these geometrically nonlinear problems. The development leads very readily to the resolution of questions pertaining to highly nonlinear problems, and the interrelations of recent emergent theories become apparent. The investigation includes evaluation of alternative approaches for numerical computations of incremental and single-step analyses and advocates specific basic approximations for particular applications.