Refined Beam Elements with only Displacement Variables andPlate/Shell Capabilities

This paper proposes a refined beam formulation with displacement variables only. Lagrange-type polynomials, in fact, are used to interpolate the displacement field over the beam cross-section. Three- (L3), four- (L4), and nine-point (L9) polynomials are considered which lead to linear, quasi-linear (bilinear), and quadratic displacement field approximations over the beam cross-section. Finite elements are obtained by employing the principle of virtual displacements in conjunction with the Unified Formulation (UF). With UF application the finite element matrices and vectors are expressed in terms of fundamental nuclei whose forms do not depend on the assumptions made (L3, L4, or L9). Additional refined beam models are implemented by introducing further discretizations over the beam cross-section in terms of the implemented L3, L4, and L9 elements. A number of numerical problems have been solved and compared with results given by classical beam theories (Euler-Bernoulli and Timoshenko), refined beam theories based on the use of Taylor-type expansions in the neighborhood of the beam axis, and solid element models from commercial codes. Poisson locking correction is analyzed. Applications to compact, thin-walled open/closed sections are discussed. The investigation conducted shows that: (1) the proposed formulation is very suitable to increase accuracy when localized effects have to be detected; (2) it leads to shell-like results in case of thin-walled closed cross-section analysis as well as in open cross-section analysis; (3) it allows us to modify the boundary conditions over the cross-section easily by introducing localized constraints; (4) it allows us to introduce geometrical boundary conditions along the beam axis which lead to plate/shell-like cases

Selection of element-wise shell kinematics using neural networks

This paper presents a novel approach to evaluate the role of non-classical effects, e.g., shear deformability, over a shell finite element model. Such an approach can identify the areas of a structural model in which the use of first-order shear deformation theories may lead to significant inaccuracies. Furthermore, it can indicate optimal distributions of structural theories over the finite element mesh to trade-off accuracy and computational costs. The proposed framework exploits the synergies among four methods, namely, the Carrera Unified Formulation (CUF), the Finite Element Method (FEM), the Node-Dependent Kinematics (NDK), and Neural Networks (NN). CUF generates the FE matrices for higher-order shell theories and provides numerical results feeding the NN for training. Via NDK, the shell theory is a property of the node; that is, a distribution of various shell theories over the FE mesh is attainable. The distributions of theories and the thickness of the structure are the inputs of multilayer NN to target natural frequencies. This work investigates the accuracy and cost-effectiveness of well-known NN. The results look promising as the NN requires a fraction of FE analyses for training, can evaluate the accuracy of FE models, and can incorporate physical features, e.g., the thickness ratio, that drives the complexity of the mathematical model. In other words, NN can inform on the FE modeling without the need to modify, rebuild, or rerun an FE model

Best Spatial Distributions of Shell Kinematics Over 2D Meshes for Free Vibration Analyses

This paper proposes a novel approach to build refined shell models. The focus is on the free vibrations of composite panels, and the node-dependent-kinematics is used to select shell theories node-wise. The methodology shown in this work can provide at least two sets of information. First, it optimizes the use of shell models by indicating the minimum number of refined models to use. Then, it highlights which areas of the structures are more vulnerable to non-classical effects. Moreover, by varying various problem features, e.g., boundary conditions, thickness, and stacking sequence, the influence of those parameters on the modelling strategy is evaluated. The results suggest the predominant influence of thickness and boundary conditions and the possibility to improve the quality of the solution via the proper use of the refinement strategy