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

Best theory diagrams for multilayered structures via shell finite elements

Abstract Composite structures are convenient structural solutions for many engineering fields, but their design is challenging and may lead to oversizing due to the significant amount of uncertainties concerning the current modeling capabilities. From a structural analysis standpoint, the finite element method is the most used approach and shell elements are of primary importance in the case of thin structures. Current research efforts aim at improving the accuracy of such elements with limited computational overheads to improve the predictive capabilities and widen the applicability to complex structures and nonlinear cases. The present paper presents shell elements with the minimum number of nodal degrees of freedom and maximum accuracy. Such elements compose the best theory diagram stemming from the combined use of the Carrera Unified Formulation and the Axiomatic/Asymptotic Method. Moreover, this paper provides guidelines on the choice of the proper higher-order terms via the introduction of relevance factor diagrams. The numerical cases consider various sets of design parameters such as the thickness, curvature, stacking sequence, and boundary conditions. The results show that the most relevant set of higher-order terms are third-order and that the thickness plays the primary role in their choice. Moreover, certain terms have very high influence, and their neglect may affect the accuracy of the model significantly

Numerical Simulation of Failure in Fiber Reinforced Composites

This paper presents numerical results concerning the failure analysis of fiber-reinforced composites. In particular, damage initiation and progressive failure are considered. The numerical framework is based on the CUF advanced structural models and the component-wise approach. Such models are employed at all scales. In other words, the same structural framework is employed for macro-, meso-, and microscales. Two approaches are assessed, including direct numerical simulations via micromechanical homogenization analysis and two-scale analysis. The results are compared with those from literature and attention is paid to the evaluation of the computational efficiency of the present numerical framework. In fact, 3D-like accuracy is sought with a reduced computational effort

Evaluation of energy and failure parameters in composite structures via a Component-Wise approach

This paper deals with the static analysis of fiber reinforced composites via the Component-Wise approach (CW). The main aim of this work is the investigation of the CW capabilities for the evaluation of integral quantities such as the strain energy, or integral failure indexes. Such quantities are evaluated in the global structures and local volumes. The integral failure indexes, in particular, are proposed as alternatives to point-wise failure indexes. The CW approach has been recently developed as an extension of the 1D Carrera Unified Formulation (CUF). The CUF provides hierarchical higher-order structural models with arbitrary expansion orders. In this work, Lagrange-type polynomials are used to interpolate the displacement field over the element cross-sections. The CW makes use of the 1D CUF finite elements to model simultaneously different scale components (fiber, matrix, laminae and laminates) with a reduced computational cost. CW models do not require the homogenization of the material characteristics nor the definition of mathematical lines or surfaces. In other words, the material characteristics of each component, e.g. fibers and matrix, are employed, and the problem unknowns are placed above the physical surface of the body. In the perspective of failure analyses, the integral evaluation of failure parameters is introduced to determine critical portions of the structure where failure could take place. Integral quantities are evaluated using 3D integration sub-domains that may cover macro- and micro-volumes of the structure. The integral quantities can be evaluated directly on fiber and matrix portions. Numerical results are provided for different configurations and compared with solid finite element models. The results prove the accuracy of the CW approach and its computational efficiency. In particular, 3D local effects can be detected. The use of the integral failure index provides qualitatively reliable results; however, experimental campaigns should be carried out to relate such indexes to the failure occurrence

Dynamic response of aerospace structures by means of refined beam theories

The present paper is devoted to the investigation of the dynamic response of typical aerospace structures subjected to different time-dependent loads. These analyses have been performed using the mode superposition method combined with refined one-dimensional models, which have been developed in the framework of the Carrera Unified Formulation (CUF). The Finite Element Method (FEM) and the principle of virtual displacements are used to compute the stiffness and mass matrices of these models. Using CUF, one has the great advantage to obtain these matrices in terms of fundamental nuclei, which depend neither on the adopted class of beam theory nor on the FEM approximation along the beam axis. In this paper, Taylor-like expansions (TE), Chebyshev expansion (CE) and Lagrange expansion (LE) have been employed in the framework of CUF. In particular, the latter class of polynomials has been used to develop pure translational displacement-based refined beam models, which are referred to as Component Wise (CW). This approach allows to model each structural component as a 1D element. The dynamic response analysis has been carried out for several aerospace structures, including thin-walled, open section and reinforced thin-shells. The capabilities of the proposed models are demonstrated, since this formulation allows to detect shell-like behavior with enhanced performances in terms of computational efforts