Abstract
The focus of this investigation is on reduced order models (ROMs) of the nonlinear geometric response of structures that are built nonintrusively, i.e., from standard outputs of commercial finite element codes. Several structures with atypical loading, boundary conditions, or geometry are considered to not only support the broad applicability of these ROMs but also to exemplify the different steps involved in determining an appropriate basis for the response. This basis is formed here as a combination of linear vibration modes and dual modes, and some of the steps involved follow prior work; others are novel aspects, all of which are covered in significant detail to minimize the expertise needed to develop these ROMs. The comparisons of the static and dynamic responses of these structures predicted by the ROMs and by the underlying finite element models demonstrate the high accuracy that can be achieved with the ROMs, even in the presence of significant nonlinearity.
Highlights
Finite element-based linear vibration analyses are commonplace in mechanical and aerospace engineering applications: they are used in early design to meet specifications and in later phases to understand and correct observed issues; they provide the structural formulation for most aeroelastic analyses, etc
Their ease of use and computational efficiency stems from three key properties of linear structural dynamic models: (1) their dynamic response can be expressed in terms of a linear combination of timeindependent mode shapes scaled by time varying generalized coordinates
The number of such combinations is, in general, very small in comparison to the number of degrees of freedom of the finite element model and does not change if the mesh is refined. (2) the governing equations for the generalized coordinates are fixed in form with coefficients that are directly extractable from the finite element model. (3) the methodology is applicable regardless of the geometry of the structure, the constitutive relation of its materials, the boundary conditions, and the specific loading
Summary
Finite element-based linear vibration analyses are commonplace in mechanical and aerospace engineering applications: they are used in early design to meet specifications and in later phases to understand and correct observed issues; they provide the structural formulation for most aeroelastic analyses, etc. The loading has often been assumed to be either uniform pressure or concentrated loads, with few studies [7,25,32] considering either a force exciting one particular mode or a non-uniformly distributed load symptomatic of an aerodynamic loading In this light, the first focus of this paper is to (i) briefly describe the construction of nonlinear geometric reduced order models (ROMs) and (ii) present detailed numerical validations in comparison with full finite element results for four novel, rather atypical, structural problems to further enrich the above database. The second part of this paper focuses on providing guidance on the details of the construction of these dual modes (see review ) to enable a non-expert to build them conveniently and efficiently
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