Combining shell and GBT-based finite elements: Linear and bifurcation analysis

A visco-elastic GBT-based finite element for steel-concrete composite beams

This work concerns the implementation of nonlinear modal reduction to flexible multi-body dynamics. Linear elastic theory will lead to instability issues with rotating beamlike structures, due to the neglecting of the membrane-bending coupling on the beam cross-section. During the past decade, considerable efforts have been focused on the derivation of geometric nonlinear formulation based on nodal coordinates. In this work, in order to improve the convergence characteristic and also to reduce the computation time in flexible multi-body dynamics, which is extremely important for complicated large systems, a standard modal reduction procedure based on matrix operation is developed with essential geometric stiffening nonlinearities retained in the equation of motion. The example used in this work is a rotating Euler-Bernoulli beam, two nonlinear reduced models were established based on modal coordinates, the first reduced model created from theoretical bending and axial mode shapes by Galerkin method; the second reduced model is derived by the standard matrix operator from a full finite element model. Transient simulation results of lower degrees of freedom from above two reduced models are compared with those obtained from full nonlinear finite element model.

There has been a growing demand for nonlinear model updating procedures in the structural dynamics community as advanced vehicles have started to incorporate nonlinearity into their designs. Finite element (FE) model updating is difficult for a nonlinear structure for several reasons: there may be many unknown parameters in the FE model so that multiple solutions may exist, and it is very expensive to compute the structure’s nonlinear normal modes from a full FE model that are an excellent metric to use for nonlinear updating. A recent work showed that some of these challenges can be overcome by updating a nonlinear reduced order model (ROM) rather than the full FE model. The updated ROM can be used to compute response statistics, stresses and ultimately life of the structure. However, one drawback of this approach is that one does not gain physical insight into which parameters in the FE model were in error, and so it is difficult to transfer the lessons learned to future FE models. This work explores the feasibility of updating a FE model to correlate with a ROM with a set of known parameters. The target ROM parameters consist of the linear stiffness and the nonlinear stiffness coefficients which have been identified previously by updating the ROM to correlate with experimental measurements. In this process an optimization routine is setup in which the free parameters are those of the FE model, such as boundary stiffness springs, imperfections, pre-stress, etc. The optimization procedure is wrapped around a ROM creation algorithm that iteratively tunes the FE parameters, creates a ROM, and evaluates the ROM parameters with respect to the target ROM in order to minimize the objective function. This work will demonstrate the procedure on a numerical example of a curved beam in order to verify its effectiveness on the nonlinear model updating.

The present study is concerned with the physical explanations of the linear and the cubic finite elements for beams and axisymmetric shells through the comparisons of their strain energy approximations with those of the Rigid Bodies-Spring Models which are the discrete elements suitable to the plastic collapse analysis using the concepts of plastic hinges and hinge lines. The established conditions for the equivalence between these two modelings, which are given as the relations between the locations of the numerical integration points and those of the occurrece of plastic hinges, can be conveniently used in the economical plastic collapse analysis of framed structures and axisymmetric shells where the locations of plastic hinge formations are controlled by the movement of numerical integration points. Some numerical results are shown in order to prove numerically the obtained relations and to verify the validity of the proposed shifting technique of numerical integration points, which is identified as 'the shifted integration technique' in the present paper.

Curved beam, plate, and shell finite elements are commonly used in the finite element modeling of a wide range of civil and mechanical engineering structures. In civil engineering, curved elements are used to model tunnels, arch bridges, pipelines, and domes. Such structures provide a more efficient load transfer than their straight/flat counterparts due to the additional strength provided by their curved geometry. The load transfer is characterized by the bending, shear, and membrane actions. In this paper, a higher-order curved inverse beam element is developed for the inverse Finite Element Method (iFEM), which is aimed at reconstructing the deformed structural shapes based on real-time, in situ strain measurements. The proposed two-node inverse beam element is based on the quintic-degree polynomial shape functions that interpolate the kinematic variables. The element is C2 continuous and has rapid convergence characteristics. To assess the element predictive capabilities, several circular arch structures subjected to static loading are analyzed, under the assumption of linear elasticity and isotropic material behavior. Comparisons between direct FEM and iFEM results are presented. It is demonstrated that the present inverse beam finite element is both efficient and accurate, requiring only a few element subdivisions to reconstruct an accurate displacement field of shallow and deep curved beams.

The application of a finite shell element for composites containing piezo-electric polymers in vibration control

Acoustic characterization of ducts lined with poroelastic materials based on wave finite element method

Constrained finite element method with displacement mapping

Finite beam element with 26 DOFs for curved composite box girders considering constrained torsion, distortion, shear lag and biaxial slip

Two methods that explicitly model airfoil geometry surface deviations for mistuning prediction in integrally bladed rotors are developed by performing a modal analysis on different degrees of freedom of a parent reduced-order model. The parent reduced-order model is formulated with Craig–Bampton component-mode synthesis in cyclic symmetry coordinates for an integrally bladed rotor with a tuned disk and airfoil geometric deviations. The first method performs an eigenanalysis on the constraint-mode degrees of freedom that provides a truncated set of interface modes, whereas the second method includes the disk fixed-interface normal mode in the eigenanalysis to yield a truncated set of ancillary modes. Both methods can use tuned or mistuned modes, where the tuned modes have the computational benefit of being computed in cyclic symmetry coordinates. Furthermore, the tuned modes only need to be calculated once, which offers significant computational savings for subsequent mistuning studies. Each geometric mistuning method relies upon the use of geometrically mistuned airfoil modes in the component-mode framework to provide a very accurate reduced-order model. Free and forced response results are compared to both the full finite-element model solutions and a traditional frequency-based approach used widely in academia and the gas-turbine industry. It is shown that the developed methods provide highly accurate results with a significant reduction in solution time compared to the full finite-element model and parent reduced-order model.

A simplified implementation of the conventional extended finite element method (XFEM) for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT) shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.

An improved model for the dynamic analysis of plates stiffened by parallel beams

The stress sensitivity analysis in conjunction with finite elements method represents an important tool for the influence analysis of the structural parameters. This analysis plays a significant role in the decision process of the formulation of the structural optimizing or probability analysis. The goal of the paper is to present theoretic and numerical aspects of the beam and shell element stress sensitivity analysis with the respect to the cross section parameters (cross section area, thickness, etc.). The whole computational procedure was inbuilt into Matlab's software module MATFEM.

A geometrically exact cross-section deformable thin-walled beam finite element based on generalized beam theory

We present an approach for formulating efficient “3D-shell elements”, which are shell finite elements that feature the same external characteristics (geometry, shape functions) as standard 3D isoparametric elements. This makes the coupling with elements sharing the same outer surfaces straightforward. In addition, these 3D-shell elements can be used with a 3D variational formulation without modifying the constitutive equation, and they are much better adapted to large strain analysis than classical shell elements.