Use of Lagrange multipliers to combine 1D variable kinematic finite elements

This paper deals with finite element problems that require different formulations in different subregions of the problem domain. Attention is focused on a variable kinematic, one-dimensional, finite element formulation which was recently introduced by the first author. Finite elements with different order of expansion over the cross-section plane are employed in different regions of the 1D domain. Lagrange multipliers are used to "mix" different elements. Constraints are imposed on displacement variables at a number of points whose location over the cross-section is a parameter of the method. The number and the location of the connection points can be modified until convergence is reached. The method is first assessed by encompassing sample problems and then it is applied to analyze a number of structures which requires different formulations in different regions. Compact, thin-walled and bridge-like sections are considered to show the effectiveness of the methodology proposed as well as its advantages to solve practical problems

Variable kinematic beam elements coupled via Arlequin method

In this work, beamelements based on different kinematic assumptions are combined through the Arlequinmethod. Computational costs are reduced assuming refined models only in those zones with a quasi-three-dimensional stress field. Variable kinematics beamelements are formulated on the basis of a unified formulation (UF). This formulation is extended to the Arlequinmethod to derive matrices related to the coupling zones between high- and low-order kinematicbeam theories. According to UF, a N-order polynomials approximation is assumed on the beam cross-section for the unknown displacements, being N a free parameter of the formulation. Several hierarchical finite elements can be formulated. Part of the structure can be accurately modelled with computationally cheap low-order elements, part calls for computationally demanding high-order elements. Slender, moderately deep and deep beams are investigated. Square and I-shaped cross-sections are accounted for. A cross-ply laminated composite beam is considered as well. Results are assessed towards Navier-type analytical models and three-dimensional finite element solutions. The numerical investigation has shown that Arlequinmethod in the context of a hierarchical formulation effectively couples sub-domains having different order finite elements without loss of accuracy and reducing the computational cos

Guidelines and Recommendations on the Use of Higher OrderFinite Elements for Bending Analysis of Plates

This paper compares and evaluates various plate finite elements to analyse the static response of thick and thin plates subjected to different loading and boundary conditions. Plate elements are based on different assumptions for the displacement distribution along the thickness direction. Classical (Kirchhoff and Reissner-Mindlin), refined (Reddy and Kant), and other higher-order displacement fields are implemented up to fourth-order expansion. The Unified Formulation UF by the first author is used to derive finite element matrices in terms of fundamental nuclei which consist of 3 × 3 arrays. The MITC4 shear-locking free type formulation is used for the FE approximation. Accuracy of a given plate element is established in terms of the error vs. thickness-to-length parameter. A significant number of finite elements for plates are implemented and compared using displacement and stress variables for various plate problems. Reduced models that are able to detect the 3D solution are built and a Best Plate Diagram (BPD) is introduced to give guidelines for the construction of plate theories based on a given accuracy and number of terms. It is concluded that the UF is a valuable tool to establish, for a given plate problem, the most accurate FE able to furnish results within a certain accuracy range. This allows us to obtain guidelines and recommendations in building refined elements in the bending analysis of plates for various geometries, loadings, and boundary conditions

A CFD/CSD interaction methodology for aircraft wings

With advanced subsonic transports and military aircraft operating in the transonic regime, it is becoming important to determine the effects of the coupling between aerodynamic loads and elastic forces. Since aeroelastic effects can significantly impact the design of these aircraft, there is a strong need in the aerospace industry to predict these interactions computationally. Such an analysis in the transonic regime requires high fidelity computational fluid dynamics (CFD) analysis tools, due to the nonlinear behavior of the aerodynamics in the transonic regime and also high fidelity computational structural dynamics (CSD) analysis tools. Also, there is a need to be able to use a wide variety of CFD and CSD methods to predict aeroelastic effects. Since source codes are not always available, it is necessary to couple the CFD and CSD codes without alteration of the source codes. In this study, an aeroelastic coupling procedure is developed to determine the static aeroelastic response of aircraft wings using any CFD and CSD code with little code integration. The aeroelastic coupling procedure is demonstrated on an F/A-18 Stabilator using NASTD (an in-house McDonnell Douglas CFD code) and NASTRAN. In addition, the Aeroelastic Research Wing (ARW-2) is used for demonstration of the aeroelastic coupling procedure by using ENSAERO (NASA Ames Research Center CFD code) and a finite element wing-box code. The results obtained from the present study are compared with those available from an experimental study conducted at NASA Langley Research Center and a study conducted at NASA Ames Research Center using ENSAERO and modal superposition. The results compare well with experimental data