The invention discloses a barrier regularization method for a nonlinear grid
distortion problem. The analysis steps of grid
distortion suppression based on unit
geometric mapping specifically comprise: obtaining input data of an analysis model, and initializing nonlinear analysis parameters; obtaining a Jacobian
determinant based on the deformation gradient, and constructing a barrier regularization function; constructing a correction
potential energy functional containing a barrier regular term, assembling the material
stiffness matrix, the geometric
stiffness matrix and the barrier
stiffness matrix to obtain a tangent stiffness matrix, and solving a nonlinear equation to update a
displacement field; if the
displacement field is not convergent, updating the
load step length and iteratively returning to calculate the deformation gradient, and if the
displacement field is convergent, outputting the displacement; and constructing a
topological optimization mathematical model, calculating an objective function value and sensitivity according to a displacement field obtained by convergence, updating
unit density, adjusting
material distribution or topological form, and outputting a final optimization structure. According to the method, unit
distortion is directly suppressed in the analysis process, the
numerical stability is enhanced, and the
topological optimization convergence performance is improved.