1,720,962 research outputs found
Modal analysis of hyperelastic structures in non-trivial equilibrium states via higher-order plate finite elements
No full textThe present work proposes a higher-order plate finite element model for the threedimensional modal analysis of hyperelastic structures. Refined higher-order 2D models are defined
in the well-established Carrera Unified Formulation (CUF) framework, coupled with the classical
hyperelastic constitutive law modeling based on the strain energy function approach. Matrix forms
of governing equations for static nonlinear analysis and modal analysis around nontrivial
equilibrium conditions are carried out using the Principle of Virtual Displacements (PVD). The
primary investigation of the following study is about the natural frequencies and modal shapes
exhibited by hyperelastic soft structures subjected to pre-stress conditions
Nonlinear analysis of hyperelastic materials and structures using higher-order finite elements
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Linearized vibration analysis of fibre-reinforced multilayered soft materials by high order 2D finite elements
No full textStress and Free Vibration Analysis of Fibre-Reinforced Soft Structures by 2D High Order Finite Elements
No full textThis study explores higher-order 2D plate finite elements for the stress and modal analysis of soft structures. The problem is established within the domain of the Carrera Unified Formulation (CUF), integrating available hyperelastic models in a unified, fully nonlinear Finite Element (FE) approach under a Total Lagrangian formulation. The matrix form of the governing equations for the nonlinear static and free vibration
analysis is carried out through the Principle of Virtual Displacements (PVD), obtaining a pure displacement-based FE model. The numerical procedure is based on a Newton-Raphson linearization approach and path-following methods. The primary objective of this research is to analyze the three-dimensional stress state of soft structures in the large strain regime and how highly nonlinear pre-stressed conditions affect natural frequencies and modal shapes. The proposed results are compared with the FE solution obtained through classical models available in commercial software.
The numerical results proposed assess the efficiency of the accuracy of higher-order 2D models for displacements, strains, and modal behaviour of soft structures
Large strain and 3D stress analysis of laminated fiber-reinforced soft material structures with high order beam finite elements
No full textThis study explores the capabilities of higher-order beam models within the Carrera Unified Formulation (CUF) framework for the large strain analysis of multilayered hyperelastic structures made of fiber-reinforced material. These materials exhibit complex mechanical behavior described by both geometrical and material nonlinearities. The proposed approach leverages the strengths of CUF, which allows for the definition of higher-order beam finite elements (FE) whose formal expression is an invariant of the structural theory adopted. The governing equations of the nonlinear static analysis are carried out by the Principle of Virtual Displacements (PVD) in a resulting pure displacement-based formulation. The nonlinear governing equations are written in matrix form in terms of Fundamental Nuclei (FN) of the internal and external force vectors and tangent stiffness matrix. The problem is solved through a Newton-Raphson linearization procedure coupled with path-following methods. The results show the capabilities of higher-order models in terms of accuracy and computational costs in predicting accurate displacements, strains, and detailed 3D stress distributions at large strain. The proposed results are compared with the FE solution obtained through classical models available in commercial software
Curvilinear 2|3D finite elements for the analysis of shells with arbitrary curvature and variable thickness
Get PDFThis paper presents a novel curvilinear finite element (FE) formulation for the static and modal analysis of shells
with arbitrary curvature and variable thickness. In the proposed approach, high-order 2D shell models are defined
in three curvilinear coordinates, exploiting the co- and contravariant components of physical quantities in the
non-orthogonal reference frame. The Carrera Unified Formulation (CUF) is adopted for the definition of 2D shell
models in which Lagrange functions are employed for the through-the-thickness approximation of displacements;
then, merging CUF with finite element approximation of midsurface, new 3D-like FE elements are generated in
which different orders of expansion can be adopted along the three curvilinear coordinates. For this reason, these
elements are referred to as 2|3-D because they present both the computational efficiency of 2D models and the capability
to model non-orthogonal geometries, such as shells with variable thickness, of 3D elements. Geometrical
relations are derived within the classical differential geometry framework, and weak-form equilibrium equations
are derived through the Principle of Virtual Displacements (PVD). The capabilities of the present finite elements
are investigated by performing the static and modal analysis of various shell-like structures. The accuracy of the
present approach in terms of three-dimensional stress states and natural frequencies is demonstrated by comparing
the numerical results with solutions obtained by classical 3D finite elements using commercial software,
highlighting the computational efficiency of the present elements. Finally, the proposed methodology is applied
to analyze complex engineering applications
High order 1D and 2D CUF models for transversely isotropic compressible and nearly-incompressible soft materials and structures
No full textIn the last decade, anisotropic materials have been the subjects of numerous studies due to their wide range of applications in mechanical, aeronautical, and civil engineering. More recent studies have shown also the great importance of the mechanical features possessed by biological–mechanical systems: micro-fluidics problems, bio-inspired material, soft rubber-like cross-ply, or biological tissue deal with these enhanced elastic properties. In this framework, the anisotropic behavior of soft material plays a crucial role: fiber-reinforced elastomeric materials, collagen fibers, muscular tissue, and blood vessels are classical examples of transversely isotropic hyperelastic materials, for which direction-dependent mechanical properties are evidenced. Constitutive equations for isotropic and transversely isotropic hyperelastic materials to model anisotropy are well established, both geometrical and material nonlinearities are taken into account, embedded in the strain energy function approach to hyperelasticity. Due to the limitations of the few available analytical solutions, nowadays finite elements procedures are the most common approach since they allow a wide range of investigations in terms of material properties and topology. The mathematical modeling of an efficient finite element formulation is a current challenging topic due to the almost-incompressible nature of hyperelastic materials: stabilized finite elements are required to contrast volumetric locking that prevents the computation of accurate stress predictions. This work proposes a new finite element formulation for the analysis of transversely isotropic (or continuous fiber-reinforced) hyperelastic materials based on Carrera Unified Formulation. The first part is devoted to the mathematical description of continuum mechanics governing equations for hyperelastic materials: the strain energy functions approach is described and strain and stress measures are here presented. The constitutive law is written in terms of invariants of the right CauchyGreen tensor, by introducing the dependence on the fiber-reinforcement direction with two additional pseudo-invariants depending on the deformation tensor. The analytical expression of the tangent elasticity tensor is carried out independently on the hyperelastic model considered. The second part is devoted to the description of refined CUF models for transversely isotropic hyperelastic materials. In our displacement-based finite element models, Carrera Unified Formulation is adopted: the primary unknown variables are discretized by adopting a recursive index notation, by coupling the classical FEM kinematic expansion with arbitrary expansion functions. The weak form of the governing equation is exploited by the Principle of Virtual Displacement in a Total Lagrangian Formulation and final equations are written in terms of fundamental nuclei, each of them independent of the chosen polynomial expansion of the displacement field, allowing rapid implementation of higher-order refined fully-nonlinear beam and plate models. The numerical solution is computed employing the Newton-Raphson linearization scheme coupled with an arc-length constraint: thus tangent stiffness matrix and internal forces vector are defined and characterized subsequently for 1D beam and 2D plate models. The last part is devoted to the validation of the numerical models by analyzing different problems in hyperelasticity, models calibration, and assessment of strain energy function models for transversely isotropic materials, establishing the capabilities of the present CUF-models in the case of highly nonlinear problems, both for the case of compressible and nearly-incompressible beams and plates, obtaining accurate results
A higher-order beam finite element for the folding analysis of composite-made booms with silicon matrix and carbon fibers
No full textThe present work proposes a unified one-dimensional finite element for the analysis of ultra-thin deployable structures made of hyperelastic material. The governing equations are derived by means of a combination of the Finite Element Method (FEM) and the Carrera Unified Formulatio (CUF). The latter allows for the derivation of the finite element arrays in a unified manner, which do not depend on the employed mathematical theory and can then be chosen as an input of the analysis. The Newton-Raphson consistent linearization scheme and the Crisfield arc-length technique are adopted to solve the geometrical nonlinear problem, which arises due to the thinness of the deployable booms. This approach is used here to analyse the buckling and post-buckling behavior of Triangular Rollable and Collapsible (TRAC) booms made of a laminated material with a silicon layer that is describe with a Neo-Hookean model. The results are finally compared to those availed in the literature, considering compressible and nearly-incompressible hyperelastic materials
Non Linear Thermo-Mechanical Numerical Model for Space Deployable Structures Actuated With Smart Materials
No full textIn this paper, a novel nonlinear finite element model is presented within the framework of the Carrera Unified Formulation (CUF) to analyse the behaviour of deployable multilayered structures actuated by smart materials like shape memory alloys (SMA) and piezoelectrics. The study focuses on the application in the aerospace industry, specifically in the development of lightweight and flexible structures for space deployable systems. The use of smart materials such as SMAs enables the structure to undergo large deformations while maintaining a high level of structural integrity and allowing for reversible shape changes under thermal and electrical stimuli. The Carrera Unified Formulation provides a powerful numerical framework for modeling the nonlinear behavior of beam structures. CUF allows for the definition of various finite element models based on structural theories by differentiating the order of expansion in the beam cross section and along the axis direction, thereby unifying different modeling approaches under a single framework. This versatility is crucial when dealing with complex material behaviour such as the phase transformations in SMA and complex geometries and characteristics of the structures considered. The model provides a detailed description of the implemented system, taking into account and large deformations. It particularly focuses on the nonlinear CUF model and the non-conventional 1D CUF elements. The first is crucial for modeling the large deformations experienced by the SMA actuator, while the latter is also useful in developing a highly accurate model of the actuator’s complex geometry without increasing the computational cost of the simulation. A thermal model, which will be integrated with the mechanical model, is currently under development. This integration aims to predict the complete physics of thermally activated shape memory actuators
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