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In this paper, topology optimization of both geometrically and materially nonlinear structure is studied using a general displacement functional as the objective function. In order to consider large deformation, effective stress and strain are expressed in terms of 2nd Piolar–Kirchhoff stress tensor and Green–Lagrange strain tensor, and constitutive equation is derived from the relation between the effective stress and strain. Sensitivity analysis of the general displacement functional is derived using the adjoint method. Numerical results of mean compliance design are compared under linear analysis, geometrical nonlinear analysis, material nonlinear analysis, and combined nonlinear analysis.