Chebyshev collocation method for the free vibration analysis of geometrically exact beams with fully intrinsic formulation

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Impact of Skeletal Malocclusion on Quality of Life

Introduction: nowadays, one of the remarkable issues in dentistry is jaw growth pattern and tooth and mouth conditions (oral conditions) on patients' quality of life and daily activities. This study was done to evaluate skeletal malocclusion effect on the quality of life and oral health in Ahvaz. Methods: 80 people with skeletal malocclusion and 80 people with normal skeletal occlusion (control) participated in this cross-sectional study. Data collection tools included: demographic and oral health impact questionnaires. Results: there is not any significant difference between average quality of life of people with Cl III and Cl II skeletal (p=0.761), but there is a meaningful relation between Cl II skeletal and normal skeletal groups and also between Cl III skeletal and normal skeletal groups (p<0.001). Conclusion: according to social and moral issues importance in raising the quality of life score and because study results showed that these patients are not in good condition of that, considering different moral and social aspects of oral condition in presenting dentistry services are suggested to develop general quality of lif

Large deflection of functionally graded porous beams based on a geometrically exact theory with a fully intrinsic formulation

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Variable stiffness composite beams subject to non-uniformly distributed loads: An analytical solution

An analytical solution is obtained for the 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads. Governing differential equations with variable coefficients, reflecting the spatially variable stiffness properties, are presented in which four degrees of freedom are fully coupled. The general analytical solution in integral form is derived and closed-form expressions obtained using series expansion approximations. The static deflection of a number of variable stiffness composite beams that can be made by fibre steering are considered with various stacking sequences. The results obtained from the proposed method are validated against numerical results from the Chebyshev collocation method and excellent agreement is observed between the two. While the proposed methodology is applicable for variable stiffness composite beams with arbitrary span-wise variation of properties, it is also an efficient approach for capturing the complicated 3D static deflection of variable stiffness composite beams subject to non-uniformly distributed loads

Static analysis of composite beams on variable stiffness elastic foundations by the homotopy analysis method

New analytical solutions for the static deflection of anisotropic composite beams resting on variable stiffness elastic foundations are obtained by the means of the Homotopy Analysis Method (HAM). The method provides a closed-form series solution for the problem described by a non-homogeneous system of coupled ordinary differential equations with constant coefficients and one variable coefficient reflecting variable stiffness elastic foundation. Analytical solutions are obtained based on two different algorithms, namely conventional HAM and iterative HAM (iHAM). To investigate the computational efficiency and convergence of HAM solutions, the preliminary studies are performed for a composite beam without elastic foundation under the action of transverse uniformly distributed loads considering three different types of stacking sequence which provide different levels and types of anisotropy. It is shown that applying the iterative approach results in better convergence of the solution compared with conventional HAM for the same level of accuracy. Then, analytical solutions are developed for composite beams on elastic foundations. New analytical results based on HAM are presented for the static deflection of composite beams resting on variable stiffness elastic foundations. Results are compared to those reported in the literature and those obtained by the Chebyshev Collocation Method in order to verify the validity and accuracy of the method. Numerical experiments reveal the accuracy and efficiency of the Homotopy Analysis Method in static beam problem

Closed-form solutions for the coupled deflection of anisotropic euler–bernoulli composite beams with arbitrary boundary conditions

The fully anisotropic response of composite beams is an important consideration in diverse applications including aeroelastic responses of helicopter rotor and wind turbine blades. Our goal is to present exact analytical solutions for the first time for coupled deflection of Euler–Bernoulli composite beams. Towards this goal, two approaches are proposed: (1) obtaining the exact analytical solutions directly from the governing equations of Euler–Bernoulli composite beams and (2) extraction of the solutions from Timoshenko composite beam solutions. For the direct solution approach, based on Euler–Bernoulli theory, new variationally-consistent field equations are obtained, in which four degrees of freedom, i.e. in-plane bending, out-of-plane bending, twist and axial elongation are fully coupled. By expressing the coupled system of differential equations in a compact matrix form, a novel expression for the eccentricity of neutral axes from the midplane, as well as the shift in shear centre from the centre of beam, is obtained. This eccentricity matrix serves to decouple the bending in the two principal directions from in-plane and twist deformations. Then, the general closed-form analytical solutions for the decoupled system are derived simply using direct integration. Additionally, the analogous closed-form analytical solutions are retrieved from the previously obtained Timoshenko composite beam solution and it is proven that they are identical to those obtained from the current direct approach for conditions where Euler–Bernoulli beam theory apply. To study the effects of anisotropy, numerical results are obtained for a number of examples with different composite stacking sequences showing various coupled behaviours. The results are compared against the Chebyshev collocation method as well as against less comprehensive analytical solutions available in the literature, noting that excellent agreement is observed, where expected. The present exact solutions can serve as benchmark problems for assessing the accuracy and convergence of various analytical and numerical method

Closed form solutions for an anisotropic composite beam on a two-parameter elastic foundation

Beams resting on elastic foundations are widely used in engineering design such as railroad tracks, pipelines, bridge decks, and automobile frames. Laminated composite beams can be tailored for specific design requirements and offer a desirable design framework for beams resting on elastic foundations. Therefore, the analysis of flexural behaviour of laminated composite beams on elastic foundations is of important consequence. Exact solutions for flexural deflection of composite beams with coupling terms between stretching, shearing, bending and twisting, resting on two-parameter elastic foundations for various types of loading and boundary conditions, are presented for the first time. The proposed new formulation is based on Euler–Bernoulli beam theory having four degrees of freedom, namely bending in two principal directions, axial elongation and twist. Governing equations and boundary conditions are derived from the principle of virtual work and expressed in a compact matrix–vector form. By decoupling bending in both principal directions from twist and axial elongation, the fourth-order differential equation for bending is derived and transformed into a system of first-order differential equations. An exact solution of this system of equations is obtained using a fundamental matrix approach. Fundamental matrices for different configurations of elastic foundation are provided. The ability of the presented mathematical model in predicting flexural behaviour of beams on elastic foundations is verified numerically by comparison with results available in the literature. In addition, the deflection of anisotropic beams is analysed for different types of stacking sequences, boundary and loading conditions. The effect of elastic foundation coefficients on the flexural behaviour is also investigated and discussed

A semi-analytical approach based on the variational iteration method for static analysis of composite beams

Using the Variational Iteration Method (VIM) the 3D static deflection problem of composite beams subject to concentrated tip and uniformly distributed loads is analysed, resulting in a system of coupled non‐ homogeneous ordinary differential equations. Using a general Lagrange multiplier, identified by variational theory, a special type of functional is constructed. By making an initial approximation in the form of a Maclaurin series and by using successive iterations, the solution in the form of convergent series is obtained. The results based on VIM are compared against those of the exact solution and Chebyshev Collocation Method (CCM) for different layups and boundary conditions and good agreement is observed between them. These results show the applicability and effectiveness of VIM for the static analysis of composite beam

Analytical plane-stress recovery of non-prismatic beams under partial cross-sectional loads and surface forces

High levels of strength- and stiffness-to-mass ratio can be achieved in slender structures by lengthwise tailoring of their cross-sectional areas. During use, a non-prismatic beam element can be subject to surface forces or loads acting on only a part of their cross-section. Practical examples involve tapered aircraft wings, wind turbine and helicopter rotor blades under fluid pressure and shear forces; arched beams in bridges subject to vehicular traction forces and tensile stresses in tendons of prestressed concrete. Presently, beam theories generalise the external loads to the entire cross-sectional area. However, this technique does not accurately describe surface-load boundary conditions and beams under partial cross-sectional loads. Hence, an efficient analytical plane-stress recovery methodology is introduced in the present study that generalises the external load to a specific sub-area of the cross-section of homogeneous non-prismatic beams with one plane of symmetry. As a result, the transverse stress components become piecewise distributions, i.e. non-smooth but continuous in the thickness direction. Additional novelties include the boundary equilibrium recovered considering applied surface loads and terms up to second-order derivatives of the internal forces to define the transverse stress field. Closed-form solutions for the specific case of non-prismatic beams with a rectangular cross-section loaded both on top and bottom surfaces are presented. For validation purposes, different numerical examples are modelled with results compared to solid-like finite element analyses as well with relevant analytical theories. The results show that the developed formulation predicts the stress field in non-prismatic beams under surface forces and non-uniform loads applied to a part of the cross-sectional area with goods levels of accuracy. The error associated with the proposed method escalates with the taper angle, such that a 10◦ taper angle could result in a 6% error at the surfaces and reduced values for interior zones, while the analytical state-of-the-art models were not able to predict the transverse stresses correctly