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.

On the Development of a Surrogate Modelling Toolbox for Virtual Assembly

“…For further research however, it might be promising to directly evaluate the R-value at the datum features. Patch Selection (CAD based) A Determination of subsets corresponding to a maximal distance to a nominal geometry such as a CAD file [74] Point set morphology Description and manipulation of the surface morphology Definition of Offset and Intersection A Definition of a certain offset between faces (e.g., to simulate adhesive gap) or of an intersection (virtual penetration) to simulate surface flattening or material loss (e.g., due to melting welding bead) [41] Morphological Filtering A Manipulate surfaces locally to simulate surface flattening due to mechanical load [51,52] Hertzian Contact Formulation A [41] Method of Influence Coefficients (MIC) A Linearized computation of elastic deformation due to mechanical load [50,57] Linear Finite Element Analysis (FEA) A Computation of elastic deformation due to mechanical load [75,76] Nonlinear FEA A Computation of elastic and plastic deformation due to mechanical load [65,66] Objective Function Searching of correspondences and the assembly position Modalities for Distance Computation Approaches to compute distances between S 1 and S 2…”

Solving basic problems of compliant tolerance analysis by static analogy

“…Although such compromise is considered acceptable in practical applications, some studies have proposed more complex methods to exploit the capabilities of advanced FEM tools, while accepting the computational burden of Monte Carlo simulation. Nonlinear FEM has been used to test more accurate contact models based on steady-state contact mechanics [39][40][41][42], friction forces [43], quadratic programming [44], sensitivity-free probability analysis [45][46][47], Timoshenko beam theory [48], and Mindlin plate theory [49,50]. Other methods combine FEM with models based on transformation vectors or matrices to deal with both rigid and flexible parts [51][52][53][54], with statistical shape models to deal with form errors [55], or with multi-objective optimization algorithms for assemblies loaded with external forces [56].…”

Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis

“…Abdelal et al 39 proposed a static stress and nonlinear explicit finite element model to simulate the riveting process of the small panels and longitudinal stiffeners. Liu et al 40,41 developed a refined nonlinear mechanical model with consideration of initial deviations and geometric nonlinearity. Liu et al 42 proposed a nonlinear variation model (NVM) to consider the geometric nonlinearity, welding shrinkage, and angular distortion based on elastic mechanics.…”