1,721,252 research outputs found
Free vibrations and bending of laminated thin plates with distorted domains in gradient elasticity: an isoparametric finite element formulation based on Hermite mapping
No full textA non-classical computational method for modelling functionally graded porous planar media using micropolar theory
Full text linkThe current study proposes a computational-based method to employ the non-classical micropolar continuum for modelling plates with in-plane functionally graded porosities. Initially, a homogenisation method is developed to derive the micropolar parameters of porous heterogenous plates based on strain energy equivalence in various designed deformations simulated via finite element analysis. The modelling procedure is further augmented to accommodate structures with functionally graded porosities. The established method offers an effective framework for studying the mechanical behaviour of porous plates with various porosity distributions and a wide range of aspect ratios. Results indicate that the micropolar theory-based modelling surpasses traditional Cauchy theory in accurately predicting the stiffness and displacement distribution of the FG porous structures. The novelty of this study lies in the integration of micropolar theory with the homogenisation of graded porosity patterns, offering enhanced predictions for materials with microstructural features. Additionally, a custom finite element formulation is developed in COMSOL to implement micropolar elasticity, significantly improving the computational efficiency to account for complex geometry, loading, and boundary conditions. To show the applicability of the method, the modelling is used to design a dental implant with its functional property mimicking that of the natural bone to avoid stress-shielding while ensuring proper occlusivity
Interaction effect of cracks on flutter and divergence instabilities of cracked beams under subtangential forces
No full textThe dynamic stability of cracked beams under conservative and non-conservative forces and for various boundary conditions is investigated. In order to extend the formulation of a previous paper by the first two authors, here doubly cracked Euler-Bernoulli beams subjected to triangularly distributed subtangential forces are considered. Cracked sections are modelled through the theory of fracture mechanics and involve a line-spring stiffness matrix. The finite element method (FEM) is used to perform numerical computations. The stability maps, obtained from the eigenvalue analysis, define the divergence and flutter domains. The proposed procedure can also tackle general multi-cracked beams
C0 FEM approximation for the thermal buckling analysis of thin plates: Lagrange Multiplier and Penalty Methods
No full textA FEM approximation for the thermal buckling of laminated thin plates employing the Lagrange Multiplier Method (LMM) and Penalty Method (PM) has been assessed. Such methods enforce internal constraints without requiring more complex formulations in a classical finite element implementation. Specifically, the thin plate assumption is applied in a first-order plate theory, eliminating the need for Hermite interpolation functions and complex meshing.
Constraints are included in the formulation via energy functions.
Applying the two methods enables the interpolation of displacement parameters using Lagrange shape functions with continuity. This approach simplifies implementation and enhances computational efficiency. \hl{In terms of model size, the Penalty Method (PM) does not introduce additional degrees of freedom (DOF). In contrast, the Lagrange Multiplier Method (LMM) increases the system's DOF due to the inclusion of Lagrange multipliers.}
For the case of LMM, the regularization method has been utilized to solve the saddle point problem.
A parametric study has been carried out for the critical buckling temperatures of laminated thin plates. To verify the effectiveness of the proposed method, results were compared with known analytical solutions and other conventional approaches, demonstrating strong agreement.
Comparing the two methods shows that both LMM and PM simplify implementing numerical algorithms for optimal solutions in computational environments
Tensile strength of the unbonded flexible pipes
No full textFlexible pipelines must be designed considering the extreme situation for which additional components are needed against severe loading and environmental conditions. Tensile armor is employed in case of high tensile forces, which increase with water depth; and massive components used against high internal and external pressures. In this paper, the mechanical behavior of the pipe under pure tension is investigated by both theoretical and numerical analysis, then the contribution of the external pressure to the axial problem is examined using an analytical analysis. As the deformations along the longitudinal direction of the studied pipe highly depend on the radial stiffness of the cross section, the influence of the pressure armor is carefully evaluated in the inception phase, and its radial stiffness is verified by its own numerical results. The plastic behavior for both steel and polymer layers is taken into account by using the secant modulus method. Moreover, this work answers a question raised by producers that need to know when tensile armor is required to reinforce Metallic Strip Flexible Pipes (MSFP). The theoretical model is employed to carry out the comparison between pipes with different configurations, in order to investigate the influencing parameters of the tensile stiffness. The results obtained from the theoretical and the numerical simulations lead to a remarkable confidence in the analytical solution thanks to a relatively small difference between the outcomes
General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels
No full textThe main aim of this paper is to provide a general framework for the formulation and the dynamic analysis computations of moderately thick laminated doubly-curved shells and panels. A 2D higher-order shear deformation theory is also proposed and the differential geometry is used to define the arbitrary shape of the middle surface of shells and panels with different curvatures. A generalized nine-parameter displacement field suitable to represent in a unified form most of the kinematical hypothesis presented in literature has been introduced. Formal comparison among various theories have been performed in order to show the differences between the well-known First-order Shear Deformation Theory (FSDT) and several Higher-order Shear Deformation Theories (HSDTs). The 2D free vibration shell problems have been solved numerically using the Generalized Differential Quadrature (GDQ) technique. The GDQ rule has been also used to perform the numerical evaluation of the derivatives of the quantities involved by the differential geometry to completely describe the reference surfaces of doubly-curved shell structures. Numerical investigations concerning four types of shell structures have been carried out. GDQ results are compared with those presented in literature and the ones obtained using commercial programs such as Abaqus. Very good agreement is observed
Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories
No full textThis paper investigates the static analysis of doubly-curved laminated composite shells and panels. A theoretical formulation of 2D Higher-order Shear Deformation Theory (HSDT) is developed. The middle surface of shells and panels is described by means of the differential geometry tool. The adopted HSDT is based on a generalized nine-parameter kinematic hypothesis suitable to represent, in a unified form, most of the displacement fields already presented in literature. A three-dimensional stress recovery procedure based on the equilibrium equations will be shown. Strains and stresses are corrected after the recovery to satisfy the top and bottom boundary conditions of the laminated composite shell or panel. The numerical problems connected with the static analysis of doubly-curved shells and panels are solved using the Generalized Differential Quadrature (GDQ) technique. All displacements, strains and stresses are worked out and plotted through the thickness of the following six types of laminated shell structures: rectangular and annular plates, cylindrical and spherical panels as well as a catenoidal shell and an elliptic paraboloid. Several lamination schemes, loadings and boundary conditions are considered. The GDQ results are compared with those obtained in literature with semi-analytical methods and the ones computed by using the finite element method
General Higher-order Equivalent Single Layer Theory for Free Vibrations of Doubly-Curved Laminated Composite Shells and Panels
No full textThe present paper provides a general formulation of a 2D higher-order equivalent single layer theory for free vibrations of thin and thick doubly-curved laminated composite shells and panels with different curvatures. The theoretical framework covers the dynamic analysis of shell structures by using a general displacement field based on the Carrera’s Unified Formulation (CUF), including the stretching and zig-zag effects. The order of the expansion along the thickness direction is taken as a free parameter. The starting point of the present general higher-order formulation is the proposal of a kinematic assumption, with an arbitrary number of degrees of freedom, which is suitable to represent most of the displacement field presented in literature. The main aim of this work is to determine the explicit fundamental operators that can be used not only for the Equivalent Single Layer (ESL) approach, but also for the Layer Wise (LW) approach. Such fundamental operators, expressed in the orthogonal curvilinear co-ordinate system, are obtained for the first time by the authors. The 2D free vibration shell problems are numerically solved using the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) techniques. GDQ results are compared with recent papers in the literature and commercial codes
Computational Approaches for Crack Propagation in Materials and Structures: Comparison Between Linear Elastic Fracture Mechanics (LEFM) and Peridynamics (PD) Based Strategies
Full text linkIn solid mechanics, the defects and imperfections of materials (e.g., cracks, dislocations, etc.) play a key role on the overall mechanical
behaviour of the structure despite their localized character. In this paper, the phenomenon of crack propagation under tension (Mode I) has
been investigated considering two different approaches: linear elastic fracture mechanics (LEFM) and bond-based peridynamics (PD). For the
former, the progression of crack path is simulated with the aid of extended finite element method (XFEM), which eliminates the need to have
conforming mesh with crack geometry by locally enriching the nodes located in the influence domain of discontinuity and singularity. For the
latter, a classical continuum mechanics-peridynamics (CCM-PD) coupling strategy is utilized to combine the ability of peridynamics in handling
the displacement field’s discontinuity with the computational efficiency of continuum-based modeling approaches. All the formulations are
developed within two-dimensional (2D) linearized framework, and implemented through in-house codes. The correspondence between LEFM
based XFEM and CCM-PD coupled models is discussed through a benchmark problem of practical importance: a uniaxially deformed finite
plate with an edge crack, focusing on the variation of fracture parameters and comparing the computational costs
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