Nonintrusive Structural Dynamic Reduced Order Modeling for Large Deformations: Enhancements for Complex Structures

Abstract

This paper focuses on the development of nonlinear reduced order modeling techniques for the prediction of the response of complex structures exhibiting “large” deformations, i.e., a geometrically nonlinear behavior, which are nonintrusive, i.e., the structure is originally modeled within a commercial finite element code. The present investigation builds on a general methodology successfully validated in recent years on simpler beam and plate structures by: (i) developing a novel identification strategy of the reduced order model parameters that enables the consideration of the large number of modes (>50 say) that would be needed for complex structures, and (ii) extending a step-by-step strategy for the selection of the basis functions used to represent accurately the displacement field. The above novel developments are successfully validated on the nonlinear static response of a nine-bay panel structure modeled with 96,000 degrees of freedom within Nastran.

Response of a Panel to Shock Impingement: Modeling and Comparison with Experiments

“…In the current study, an alternate approach [20] that uses the tangent stiffness matrix for each combination of load/prescribed displacement is employed to determine the stiffness coefficients. This approach uses an N m × N m matrix instead of the full order stiffness matrix and therefore represents a saving of computational effort.…”

Prediction of displacement and stress fields of a notched panel with geometric nonlinearity by reduced order modeling

“…Equation (5) (4) and imposing the condition that the error be orthogonal to the basis (Galerkin approach), a set of nonlinear ordinary differential equations for the generalized coordinates ( ) t q n can be obtained [8], they are the reduced order model equations [8]. They can be used for their estimation (see [26]) but an indirect evaluation of many of these coefficients from the finite element model is also possible (see [1,8,22,29]) and is adopted here.…”

“…The basis functions resulting from this process are the "dual modes" [8] to be appended to the linear modes to form the basis. The appropriateness of these modes can be assessed as in [29] by comparing the displacements induced by the loads of Eqs (11) and (12) and by physical (static or dynamic) loads in sections of the N dimensional space, where N denotes the number of degrees of freedom of the structure. This comparison will be successfully carried out in the reduced order model construction section.…”

“…These modes are finally added to the linear modes (step 7) to form the final basis. The process is completed (step 8) by the evaluation of the stiffness coefficients according to one of the methodologies described in [1,8,22,29]. The imposed displacement method of [22] as modified in [4,5,8] was selected here.…”

“…Before proceeding with detailed validations of the reduced order models, it is desirable to assess the adequacy of the dual modes to represent the in-plane displacements induced by the large transverse motions. To this end, it was proposed in [29] to compare the part of the threedimensional space occupied by three representative displacements obtained in various finite element computations to the similar space generated by the dual modes. In the present example, these three displacements were selected as the transverse displacement at the midpoint of the beam and the transverse and in-plane displacements at the notch tip.…”