1,721,004 research outputs found
Modelling stress-corrosion microcracking in polycrystalline materials by the Boundary Element Method
Full text linkThe boundary element method is employed in this study in conjunction with the finite element method to build a multi-physics hybrid numerical model for the computational study of stress corrosion cracking related to hydrogen diffusion in polycrystalline microstructures. More specifically a boundary integral representation is used to represent the micro-mechanics of the aggregate while an explicit finite element method is used to model inter-granular hydrogen diffusion. The inter-granular interaction between contiguous grains is represented through cohesive laws, whose physical parameters depend on the concentration of inter-granular hydrogen, diffusing along the interfaces according to the Fick's second law. The model couples the effectiveness of the polycrystalline boundary element micro-mechanics model with the generality of the finite element representation of the inter-granular diffusion process. Few numerical tests are reported, to demonstrate the potential of the proposed technique
Nonlinear free vibrations of composite structures via the X-Ritz method
No full textThe analysis of large amplitude vibrations of thin-walled cracked structures build as plate assembly
is considered in this study. The problem is addressed via a Ritz approach, called X-Ritz, based
on the first order shear deformation theory and von K ́arm ́an’s geometric nonlinearity assumptions.
The trial functions are expressed as series of regular orthogonal polynomial products supplemented
with special functions able to represent the crack behaviour; boundary functions are used to guarantee
the fulfillment of the kinematic boundary conditions. Results are presented, which illustrate
the influence of cracks on the stiffening effect due to large amplitude vibrations
Virtual element method for damage modelling of two-dimensional metallic lattice materials
Full text linkAdditively-manufactured metallic lattice materials are a class of architectured solids that is becoming increasingly popular due to their unique cellular structure, which can be engineered to meet specific design requirements. Understanding and modelling the damage in these innovative materials is a significant challenge that must be addressed for their effective use in aerospace applications. The Virtual Element Method (VEM) is a numerical technique recently introduced as a generalisation of the FEM capable of handling meshes comprising an assemblage of generic polytopes. This advantage in creating domain discretisation has already been used to model the behaviour of materials with complex microstructures. This work employs a numerical framework based on a nonlinear VEM formulation combined with a continuum damage model to study the fracture behaviour of two-dimensional metallic lattice material under static loading. VEM's effectiveness in modelling lattice failure behaviour is assessed through several numerical tests. The influence of micro-architecture on the material's failure behaviour and macroscopic mechanical performance is discussed
Nonlinear free vibrations analysis of cracked composite stiffened plates via X-Ritz approach
No full textThin and moderately thick composite multi-layered plates are widely employed in naval and aerospace
structures. They can experience the presence of cracks, generated for example by corrosion, fatigue
or accidental external causes, which aect their static and dynamic behaviour. As regard the dynamic
characteristics of plates, many studies have focused on the linear vibration analysis of both isotropic
and composite thin and thick plates, providing for a comprehensive knowledge of the plate dynamic
behaviour. However, for an accurate appraisal of the plate dynamics, in some applications it is needed
to investigate the nonlinear free vibration problem; a literature survey evidences that the large amplitude
vibrations have received considerable attention for single plate congurations. Dierent approaches have
been proposed to model cracked plates and, among others, the Ritz method shows adequate accuracy
and computational eciency. To apply the Ritz method to crack problems by using standard admissible
functions the sub-structuring or multi-domain strategy has been employed. More recently, the Ritz
approach has been proposed with special trial functions, which account for the presence of the crack by
describing the discontinuity of the solution across the crack and the tip singularity [1,2]. In the present
work, nonlinear free vibrations of cracked stiened composite plates are investigated by modelling the
problem by the X-Ritz formulation recently presented by the authors [3]. In the framework of the rst
order shear deformation theory, this formulation combines the features of both the Ritz method and the
X-FEM strategy, as it employs variables approximations obtained by enriching the Ritz series expansion
with suitably dened crack functions. This modelization applies to a single quadrangular plate and is
coupled with a multi-domain approach which open towards an ecient modelization of stiened panels
and thin-walled structures. Thus, the entire structure is modelled as individual, separated plates which
can contain cracks; these plates are then joined by enforcing the continuity conditions along the common
edges through penalty techniques. This approach has: (i) the advantage of a very simple pre-processing
stage, as it only requires the geometrical information on the plates that compose the structure and the
cracks locations; (ii) the feature to incorporate the singular behaviour at the crack tips. Convergence
and accuracy studies on linear and nonlinear free vibrations of uncracked congurations are carried out
on uncracked congurations to validate the approach by comparison with literature and nite elements
results. Cracked stiened panels nonlinear free vibrations results are then presented to discuss the
potential of the method.
References
1. Milazzo, A., Benedetti, I., Gulizzi, V. (2018). An extended
Ritz formulation for buckling and post-buckling analysis of cracked multilayered plates. Composite
Structures, 201, 980-994.
2. Milazzo, A., Benedetti, I., Gulizzi, V. (2019). A single-domain Ritz
approach for buckling and post-buckling analysis of cracked plates. International Journal of Solids and
Structures, 159, 221-231.
3. Gulizzi, V., Oliveri, V., Milazzo, A. (2019), Buckling and post-buckling
analysis of cracked stiened panels via an X-Ritz method. Aerospace Science and Technology, in pres
Microcracking in piezoelectric materials by the Boundary Element Method
Full text linkA 3D boundary element model for piezoelectric polycrystalline micro-cracking is discussed in this contribution. The model is based on the boundary integral representation of the electro-mechanical behavior of individual grains and on the use of a generalized cohesive formulation for inter-granular micro-cracking. The boundary integral formulation allows to address the electro-mechanical boundary value problem in terms of generalized grain boundary and inter-granular displacements and tractions only, which implies the natural inclusion of the cohesive laws in the formulation, the simplification of the analysis pre-processing stage, and the reduction of the number of degrees of freedom of the overall analysis with respect to other popular numerical methods
High-order accurate transient and free-vibration analysis of plates and shells
No full textThe limited availability of analytical solutions and the high cost associated with experimental testing motivate the use of computational tools to assess the dynamic behavior of load-bearing components, especially when a wide design space must be explored, as is often the case with composite structures. In this context, a novel high-order accurate discontinuous Galerkin formulation for transient and free-vibration analysis of multilayered plates and shells is presented and numerical validated. The starting point of the formulation is a generalized structural theory for multilayered shells with arbitrary curvature based on the expansion of the displacement covariant components throughout the shell thickness. The variational statement of three-dimensional elastodynamics allows deriving the strong form of the governing differential equations, which form the basis to obtain the corresponding discontinuous Galerkin weak statements. As the order of the through-the-thickness expansion and the order of the discontinuous Galerkin basis functions are free parameters, the proposed approach allows tuning the order of accuracy of the computed solution throughout both the shell thickness and the shell modeling domain. Numerical results are reported and discussed for several validation test cases in terms of h- and p-convergence analyses, demonstrating the high-order accuracy, robustness, and computational savings of the formulation
Computational Homogenization of Heterogeneous Materials by a Novel Hybrid Numerical Scheme
Full text linkThe Virtual Element Method (VEM) is a recent numerical technique capable of dealing with very general polygonal
and polyhedral mesh elements, including irregular or non-convex ones. Because of this feature, the VEM ensures noticeable
simplification in the data preparation stage of the analysis, especially for problems whose analysis domain features complex
geometries, as in the case of computational micro-mechanics problems. The Boundary Element Method (BEM) is a well-known,
extensively used and effective numerical technique for the solution of several classes of problems in science and engineering. Due
to its underlying formulation, the BEM allows reducing the dimensionality of the problem, resulting in substantial simplification
of the pre-processing stage and in the reduction of the computational effort, without jeopardising the solution accuracy. In this
contribution, we explore the possibility of a coupling VEM and BEM for computational homogenisation of heterogeneous materials
with complex microstructures. The test morphologies consist of unit cells with irregularly shaped inclusions, representative e.g. of
a fibre-reinforced polymer composite. The BEM is used to model the inclusions, while the VEM is used to model the surrounding
matrix material. Benchmark finite element solutions are used to validate the analysis results
A discontinuous Galerkin formulation for variable angle tow composite plates higher-order theories
No full textA discontinuous Galerkin formulation for the mechanical behaviour of Variable
Angle Tow multi-layered composite plates is presented. The starting point of the
formulation is the strong form of the governing equations, which are obtained by means
of the Principle of Virtual Displacement, the Generalized Unified Formulation and the
Equivalent Single Layer assumption for the mechanical behaviour of the whole assembly.
To obtain the corresponding discontinuous Galerkin formulation, an auxiliary flux variable
is introduced and the governing equations are rewritten as a first-order system of
partial differential equations. To link neighbouring mesh elements, suitably defined numerical
fluxes are introduced and an Interior Penalty discontinuous Galerkin formulation
is obtained and presented. hp-convergence analyses for straight-fiber composite plates
and a comparison with the results available in the literature for variable angle tow plates
show the accuracy of the proposed formulation as well as the computational savings in
terms of overall degrees of freedom
Ritz Model for Damage Analysis in Variable Angle Tow Composite Plates
Full text linkIn this work, a Ritz method is developed for progressive damage analysis of multilayered variable angle tow (VAT) composite plates under geometrically non-linear strains. The proposed model adopts a first order shear deformation theory and considers geometric non-linearities through the von Karman assumptions. A meso-modelling approach based on Continuum Damage Mechanics is adopted for analysing the initiation and evolution of damage. The onset of damage is predicted using the Hashin’s criteria. Four damage indices are defined and computed for expressing the degradation of the mechanical properties of the material, both for fibers and matrix under either tension and compression loading. A set of numerical tests is carried out to validate the model, assess its convergence and show its capabilities, eventually presenting novel results for progressive non-linear damage in variable angle tow composite plates
Damage Detection in Truss Structures Using Modal Expansion and Flexibility Matrix
No full text. In this study, a new index for damage detection in truss structures is
presented. The technique exploits incomplete mode shapes obtained from pseu do-experimental data which mimic the records of a limited number of sensors
placed on the structure. The modes are completed using a multi-step modal ex pansion technique based on the subspace iteration method. Stiffness and mass
matrices are computed only after the dynamic condensation matrix converges,
thus making the iteration procedure computationally efficient. Once the modes
are expanded and mass normalized, the identification method is developed by
computing the flexibility matrices of healthy and damaged structures. Each
flexibility matrix is approximated as the product of the first circular frequencies
and complete mode shapes of the truss where each column represents the node
displacements associated with unitary forces applied to the corresponding de gree of freedom. From the flexibility matrix, it is possible to construct a matrix
of strain changes induced by the presence of damage in the structure. The dam age identification exploits a novel index based on Singular Value Decomposi tion of the strain change matrix and identifies the damaged elements as bars
with the highest values. Two numerical examples on planar truss structures
show the potentialities of the method
- …
