Compliant assembly analysis including initial deviations and geometric nonlinearity—Part I: Beam structure

Abstract

In the past decades, several compliant assembly analysis models have been developed to consider structural deformations during assembly progresses. Available methods address the influence of linear elastic deformations, whereas for the case of large-scale flexible structures with complex boundary conditions, the geometric nonlinearity will be a significant factor affecting the accuracy of assembly variation prediction. This paper introduces a refined mechanical model to develop a variation analysis method for beam structures. Based on the Timoshenko theory, governing equations of flexible beam are obtained by using the principle of virtual work with consideration of initial deviations and a von Kármán type of kinematic nonlinearity. Moreover, corresponding finite element formulas are presented, which also can be degenerated into non-initial deviation form or the linearized form. With the nonlinear beam model, an assembly variation analysis method is proposed for beam structures, which takes initial deviations, fixture errors, and matching deviations into account. Case studies of static loading analysis and slender beam assembly springback analysis are demonstrated to verify the feasibility and accuracy of the presented method.