Boundary constraint static model modification of beam structure based on homotopy stochastic finite element method

Considering the uncertainty associated with structural boundary conditions, a method for modifying the boundary constraint static model of beam structures was proposed based on the homotopy stochastic finite element method. The overall modification of both the beam body elements and boundary elements was achieved using uncertain static measurement data. By employing the static condensation method, computational degrees of freedom were ensured to match measured degrees of freedom. Regularization methods were applied to mitigate ill-conditioned solutions in modification equations for stochastic models. The probabilistic residual minimization method enables optimal selection of homotopy coefficients, ensured accurate identification of boundary constraints and precise overall modification. Finally, simulations on variable-section concrete beams and static loading tests on aluminum alloy beams were conducted to verify the effectiveness of this approach.