High-Fidelity 1D and 2D Models for Static and Dynamic Analyses of Wind Turbine Rotor Blades

Wind energy is an essential renewable source to tackle the most critical environmental problems, such as global warming. Recently, the wind blade size has been increasing to maximize turbine efficiency. However, increased dimensions lead to further design challenges due to severe loadings - inertial and aerodynamic - and unavoidable manufacturing complexities. Therefore, extensive simulation campaigns covering as many operational conditions as possible become crucial for sustainable design and manufacturing. Various numerical tools for this purpose have been proposed to predict the response and damage levels of sizeable composite wind turbine blades. Within this context, this paper presents results based on the Carrera Unified Formulation (CUF) on various blade configurations. The CUF is a hierarchical formulation providing classical and higher-order beam, plate, and shell models using arbitrary kinematic expansions. The one-dimensional (1D) and two-dimensional (2D) CUF-based models can ensure a similar accuracy of three-dimensional (3D) solutions with considerable savings in computational efforts. The principle of virtual work and a finite element approximation is used to formulate both geometrically linear and nonlinear governing equations. The numerical results focus on static, dynamic, and failure analyses performed on composite wind turbine blades. The failure index evaluation uses a global/local approach that combines the CUF models with conventional FE solutions. In addition, future challenges related to health monitoring, damage detection, and developing a digital twin for structural verification will be discussed

Thermoelastic micromechanical analysis of CFRP with voids

The work investigates the effect of dispersed air gaps – voids – within the matrix on the local stress and strain fields and the influence on the thermoelastic properties of carbon fiber reinforced plastic polymers (CFRPs). The micromechanics framework is based on the use of 1D higher-order structural theories obtained via the Carrera Unified Formulation (CUF) and periodic boundary conditions (PBC), including plasticity over the matrix. Voids are randomly generated within the matrix, considering different volume fractions. Moreover, several distributions at the same void volume fraction permit to perform statistical analyses of the results. Based on numerical results, increasing void fractions leads to higher stress and strain values. Regarding the thermoelastic properties, the results show a good agreement with the benchmarks, thus confirming that voids have a remarkable effect on thermoelastic properties

AN ANALYTICAL TOOL FOR STUDYING THE IMPACT OF PROCESS PARAMETERS ON THE MECHANICAL RESPONSE OF COMPOSITES

The present work presents a numerical framework able to predict the impact of the manufacturing process on the mechanical performance of the composite component. A simple one-dimensional thermochemical model has been used to predict the evolution of the degree of cure of the resin for a given thermal cycle. The homogenized properties at the lamina level have been obtained through a classical mixtures law and employed to predict the process-induced deformations. A refined one-dimensional model, derived in the framework of the Carrera Unified Formulation, has been used to provide accurate results with reduced computational costs. The virtual manufacturing framework has been used to investigate the impact of the process parameters on process-induced defects of a simple composite part. Different curing cycles have been considered and their outcomes discussed. The results demonstrate the capability of the present numerical tool to correlate the manufacturing process parameters with the mechanical performances of the final component

Mesh objective characteristic element length for higher-order finite beam elements

The use of fracture energy regularization techniques can effectively mitigate the mesh dependency of numerical solutions caused by the strain softening behavior of quasi-brittle materials. However, the successful regularization depends on the correct estimation of the crack bandwidth in Finite Element solutions. This paper aims to present an enhanced crack band formulation to overcome the strain localization instability especially for the higher-order elements developed in the framework of Carrera Unified Formulation (CUF). Besides, a modified Mazars damage method incorporating fracture energy regularization is employed to describe the nonlinear damage behavior of the concrete. To evaluate the efficiency of the proposed crack band formulation, three experimental concrete benchmarks are selected for the numerical damage analysis. By comparing numerical and experimental results, the proposed method can guarantee mesh objectivity despite varying finite element numbers and orders, indicating perseved fracture energy consumption within proposed higher-order beam models

Evaluation of transverse shear stresses in layered beams/plates/shells via stress recovery accounting for various CUF-based theories

This paper exploits the stress recovery technique to evaluate the out-of-plane stress components in the static analysis of composite beams, plates and shells. This technique is implemented in the framework of the Carrera Unified Formulation, an approach allowing the implementation of the theories of structures in a compact way. This work uses Taylor, Legendre and Jacobi polynomials with equivalent single-layer and layer-wise approaches. The finite element method is applied to provide numerical solutions. Multi-layered beams, plates and shells subjected to different loading and boundary conditions are studied to validate and assess the proposed technique. The results are compared with those from the literature and show that the stress recovery technique provides reasonable accuracy for the shear stresses, even with lower-order models. Furthermore, results confirm that, when dealing with thick structures, the adoption of layer-wise models is mandatory to obtain accurate results

Static analysis of thin-walled beams accounting for nonlinearities

This paper presents numerical results concerning the nonlinear analysis of thin-walled isotropic structures via 1D structural theories built with the Carrera Unified Formulation (CUF). Both geometrical and material nonlinearities are accounted for, and square, C- and T-shaped beams are considered. The results focus on equilibrium curves, displacement, and stress distributions. Comparisons with literature and 3D finite elements (FE) are provided to assess the formulation’s accuracy and computational efficiency. It is shown how 1D models based on Lagrange expansions of the displacement field are comparable to 3D FE regarding the accuracy but require considerably fewer degrees of freedom

Compressive damage modeling of fiber-reinforced composite laminates using 2D higher-order layer-wise models

A refined progressive damage analysis of fiber-reinforced laminated composites subjected to compressive loads is presented here. The numerical analysis exploits higher-order theories developed using the Carrera Unified Formulation, specifically 2D plate theories with Lagrange polynomials to enhance the kinematic approximation through each ply’s thickness resulting in a layer-wise structural model. The CODAM2 material model, based on continuum damage mechanics, governs the intralaminar composite damage. The Hashin criteria and the crack-band approach provide failure initiation and propagation, respectively. Fiber micro-buckling and kinking are taken into account via the use of nonlinear post-peak softening models. It is shown that linear-brittle stress-strain softening is effective for accurate compressive strength predictions. A series of numerical assessments on coupon level composite laminates is carried out to verify the proposed numerical framework while its validation is demonstrated by successfully applying the numerical tool to test cases for which experimental data is available from the literature. Various through-the-thickness structural models are evaluated to provide insights for proper modeling. Numerical assessments considered quasi-isotropic laminates, the compressive strength, and size-effects under brittle fracture of notched laminates, and progressive damage characteristics due to stable crack growth in compact compression tests. The results show the possibility of using coarser meshes than those used in standard FEM approaches as the accuracy of predictions is preserved through the use of higher-order structural theories