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Danilo H Konda - One of the best experts on this subject based on the ideXlab platform.
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a bem formulation based on reissner s hypothesis for analysing the coupled stretching Bending Problem of building floor structures
Engineering Analysis With Boundary Elements, 2012Co-Authors: Gabriela Fernandes, Danilo H KondaAbstract:Abstract In this work, a plate Bending formulation of the boundary element method (BEM) based on the Reissner's hypothesis to perform linear analysis of plates reinforced by rectangular beams is extended to consider the beams not displayed over their middle surface. Therefore eccentricity effects are taken into account. The building floor structure is modelled as a stiffened plate which is treated as a single body without dividing it into beam and plate elements. Moreover the equilibrium and compatibility conditions are automatically imposed by the integral equations. In the proposed model the final system of equation is obtained by coupling the Bending Problem to the stretching Problem. Besides, in order to reduce the number of degrees of freedom, both the displacements and tractions are approximated along the beam width, leading to a model where the values are defined on the beams axis. In order to validate the proposed formulation, the numerical results are compared to a well know finite element code.
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a bem formulation for analysing the coupled stretching Bending Problem of plates reinforced by rectangular beams with columns defined in the domain
Computational Mechanics, 2010Co-Authors: Gabriela Fernandes, Guido J Denipotti, Danilo H KondaAbstract:In this work, a boundary element formulation to analyse plates reinforced by rectangular beams, with columns defined in the domain is proposed. The model is based on Kirchhoff hypothesis and the beams are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The presented boundary element method formulation is derived by applying the reciprocity theorem to zoned plates, where beams are treated as thin sub-regions with larger rigidities. The integral representations derived for this complex structural element consider the Bending and stretching effects of both structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed, being the Bending tractions eliminated along interfaces. The in-plane tractions and the Bending and in-plane displacements are approximated along the beam width, reducing the number of degrees of freedom. The columns are introduced into the formulation by considering domain points where tractions can be prescribed. Some examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with other numerical solutions.
Gabriela Fernandes - One of the best experts on this subject based on the ideXlab platform.
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a bem formulation based on reissner s hypothesis for analysing the coupled stretching Bending Problem of building floor structures
Engineering Analysis With Boundary Elements, 2012Co-Authors: Gabriela Fernandes, Danilo H KondaAbstract:Abstract In this work, a plate Bending formulation of the boundary element method (BEM) based on the Reissner's hypothesis to perform linear analysis of plates reinforced by rectangular beams is extended to consider the beams not displayed over their middle surface. Therefore eccentricity effects are taken into account. The building floor structure is modelled as a stiffened plate which is treated as a single body without dividing it into beam and plate elements. Moreover the equilibrium and compatibility conditions are automatically imposed by the integral equations. In the proposed model the final system of equation is obtained by coupling the Bending Problem to the stretching Problem. Besides, in order to reduce the number of degrees of freedom, both the displacements and tractions are approximated along the beam width, leading to a model where the values are defined on the beams axis. In order to validate the proposed formulation, the numerical results are compared to a well know finite element code.
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a bem formulation for analysing the coupled stretching Bending Problem of plates reinforced by rectangular beams with columns defined in the domain
Computational Mechanics, 2010Co-Authors: Gabriela Fernandes, Guido J Denipotti, Danilo H KondaAbstract:In this work, a boundary element formulation to analyse plates reinforced by rectangular beams, with columns defined in the domain is proposed. The model is based on Kirchhoff hypothesis and the beams are not required to be displayed over the plate surface, therefore eccentricity effects are taken into account. The presented boundary element method formulation is derived by applying the reciprocity theorem to zoned plates, where beams are treated as thin sub-regions with larger rigidities. The integral representations derived for this complex structural element consider the Bending and stretching effects of both structural elements working together. The standard equilibrium and compatibility conditions along interface are naturally imposed, being the Bending tractions eliminated along interfaces. The in-plane tractions and the Bending and in-plane displacements are approximated along the beam width, reducing the number of degrees of freedom. The columns are introduced into the formulation by considering domain points where tractions can be prescribed. Some examples are then shown to illustrate the accuracy of the formulation, comparing the obtained results with other numerical solutions.
Shenjie Zhou - One of the best experts on this subject based on the ideXlab platform.
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a flexoelectric spherical microshell model incorporating the strain gradient effect
Applied Mathematical Modelling, 2019Co-Authors: Shenjie ZhouAbstract:Abstract In this paper, a size-dependent flexoelectric spherical microshell model is proposed considering flexoelectric effect and strain gradient effect. By means of the variation principle, explicit expressions of the governing equations and the boundary conditions are deduced. Solving corresponding governing equations, analytical solutions of both direct and converse flexoelectric responses in static axisymmetric Bending Problem are obtained. Then, the flexoelectric responses in barium strontium titanate spherical microshells with and without a circular top opening are numerically investigated. Both the direct and converse flexoelectric responses are found to vary non-monotonically as the central angle increases. The converse flexoelectric Bending is examined to exist even in clamped spherical microshells, which is different from the case of flat structures. In addition, for all cases, the strain gradient effect will highly reduce the flexoelectric responses, particularly when the thickness approaches the material internal scale constants.
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a size dependent model for bi layered kirchhoff micro plate based on strain gradient elasticity theory
Composite Structures, 2014Co-Authors: Shenjie Zhou, Shasha Zhou, Binglei WangAbstract:Abstract A size-dependent model for bi-layered Kirchhoff micro-plate is developed based on the strain gradient elasticity theory. The governing equations and boundary conditions are derived by using the variational principle. To illustrate the new model, the Bending Problem of a simply supported bi-layered square micro-plate subjected to constant distributed load is solved. Numerical results reveal that the deflection and axial stress decrease remarkably compared with the classical plate results, and the zero-strain surface deviates significantly from the conventional position, when the thickness of plate is comparable to the material length scale parameters. The size effects, however, are almost diminishing as the thickness of plate is far greater than the material length scale parameters. In addition, the bi-layered plate can be simplified to the monolayer plate as the thickness of one layer is becoming much greater than that of the other layer.
Norman F. Knight - One of the best experts on this subject based on the ideXlab platform.
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A refined first-order shear-deformation theory and its justification by plane strain Bending Problem of laminated plates
International Journal of Solids and Structures, 1996Co-Authors: Norman F. KnightAbstract:Abstract A refined first-order shear-deformation theory is proposed and used to solve the plane strain Bending; Problem of both homogeneous plates and symmetric cross-ply laminated plates. In Reissner-Mindlin's traditional first-order shear-deformation theory (FSDT), the displacement field assumptions include a linear inplane displacement component and a constant transverse deflection through the thickness. These assumptions are retained in the present refined theory. However, the associated transverse shear strain derived from these displacement assumptions, which is still independent of the thickness coordinate, is endowed with new meaning—the stress-weighted average shear strain through the thickness. The variable distribution of transverse shear strain is assumed in such a way that it agrees with the shear stress distribution derived from the integration of equilibrium equation. This paper introduces the effective transverse shear stiffness of plates by assuming that the normalized distribution of through-the-thickness transverse shear stress remains unchanged regardless of geometrical configuration (span-to-thickness ratio) for plane-strain Bending Problem, which is justified by the exact elasticity solution. Without losing the simplicity of the displacement field assumptions of Reissner-Mindlin's FSDT, the present refined first-order theory not only shows improvement on predicting deflections but also accounts for a variable transverse shear strain distribution through the thickness. In addition, all the boundary conditions, equilibrium equations, and constitutive relations are satisfied pointwise. Comparisons of deflection, transverse shear strain, and transverse shear stress obtained using the present theory are made with the exact results given by Pagano.
Hong Yuan - One of the best experts on this subject based on the ideXlab platform.
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R-function Theory for Bending Problem of Shallow Spherical Shells with Polygonal Boundary
Civil Engineering Journal, 2020Co-Authors: Hong Yuan, Xiongfei Yang, Huanliang Zhang, Qifeng PengAbstract:The governing differential equations of the Bending Problem of simply supported shallow spherical shells on Winkler foundation are simplified to an independent equation of radial deflection. The independent equation of radial deflection is decomposed to two Laplace operators by intermediate variable. The R-function theory is applied to describe a shallow spherical shell on Winkler foundation with concave boundary, and then a quasi-Green’s function is established by using the fundamental solution and the normalized boundary equation. The quasi-Green’s function satisfies the homogeneous boundary condition of the Problem. The Laplace operators of the Problem are reduced to two simultaneous Fredholm integral equations of the second kind by the Green’s formula. The singularity of the kernel of the integral equation is eliminated by choosing a suitable form of the normalized boundary equation. The integral equations are discretized into the homogeneous linear algebraic equations to proceed numerical computing. The singular term in the discrete equation is eliminated by the integral method. Some numerical examples are given to verify the validity of the proposed method in calculating simple boundary conditions and polygonal boundary conditions. A comparison with the ANSYS finite element (FEM) solution shows a good agreement, and it demonstrates the feasibility and efficiency of the present method.
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application of the r function theory for the Bending Problem of shallow spherical shells with a dodecagon domain
Advanced Materials Research, 2012Co-Authors: Hong YuanAbstract:The R-function theory is applied to describe the dodecagon domain of shallow spherical shells on Winkler foundation, and it is also used to construct a quasi-Green’s function. The quasi-Green’s function satisfies the homogeneous boundary condition of the Problem. Then the differential equation of the Problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Green’s formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. A comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the present method.
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a quasi green s function method for the Bending Problem of simply supported trapezoidal shallow spherical shells on winkler foundation
Advanced Materials Research, 2012Co-Authors: Hong YuanAbstract:The quasi-Green’s function method (QGFM) is applied to solve the Bending Problem of simply supported trapezoidal shallow spherical shells on Winkler foundation. A quasi-Green’s function is established by using the fundamental solution and the boundary equation of the Problem. And the function satisfies the homogeneous boundary condition of the Problem. Then the differential equation of the Problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Green’s formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the proposed method.
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green quasifunction method for Bending Problem of clamped orthotropic trapezoidal thin plates on winkler foundation
Applied Mechanics and Materials, 2011Co-Authors: Hong YuanAbstract:The Green quasifunction method (GQM) is applied to solve the Bending Problem of clamped orthotropic thin plates with trapezoidal boundary shape on Winkler foundation. Firstly the governing differential equation of the Problem is reduced to the boundary value Problem of the biharmonic operator, and then it is reduced to the Fredholm integral equation of the second kind by Green’s formula. A Green quasifunction is established by using the fundamental solution and the boundary equation of the Problem. This function satisfies the homogeneous boundary condition of the Problem. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with ANSYS finite element solution shows good agreement. The proposed method is a novel and effective mathematical one.
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green quasifunction method for Bending Problem of clamped orthotropic thin plates with trapezoidal boundary shape
Applied Mechanics and Materials, 2011Co-Authors: Hong YuanAbstract:The Green quasifunction method(GQM) is employed to solve the Bending Problem of clamped orthotropic thin plates with trapezoidal boundary shape. Firstly the governing differential equation of the Problem is reduced to the boundary value Problem of the biharmonic operator, and then it is reduced to the Fredholm integral equation of the second kind by Green’s formula. A Green quasifunction is established by using the fundamental solution and the boundary equation of the Problem. This function satisfies the homogeneous boundary condition of the Problem. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. A numerical example demonstrates the feasibility and efficiency of the proposed method, and it is a novel mathematical method.