Search results for " Kirchoff"

showing 2 items of 2 documents

Exact and approximate analytical solutions for nonlocal nanoplates of arbitrary shapes in bending using the line element-less method

2021

AbstractIn this study, an innovative procedure is presented for the analysis of the static behavior of plates at the micro and nano scale, with arbitrary shape and various boundary conditions. In this regard, the well-known Eringen’s nonlocal elasticity theory is used to appropriately model small length scale effects. The proposed mesh-free procedure, namely the Line Element-Less Method (LEM), only requires the evaluation of simple line integrals along the plate boundary parametric equation. Further, variations of appropriately introduced functionals eventually lead to a linear system of algebraic equations in terms of the expansion coefficients of the deflection function. Notably, the prop…

Harmonic polynomials Kirchoff plate Line element-less method Meshfree method Nonlocal elasticityLine elementMechanical EngineeringMathematical analysisLinear systemLine integral02 engineering and technology021001 nanoscience & nanotechnologyCondensed Matter PhysicsAlgebraic equation020303 mechanical engineering & transports0203 mechanical engineeringSettore MAT/05 - Analisi MatematicaMechanics of MaterialsDeflection (engineering)Line (geometry)Settore MAT/03 - GeometriaBoundary value problemSettore ICAR/08 - Scienza Delle Costruzioni0210 nano-technologyParametric equationMathematicsMeccanica
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Characteristic matrix in the bending plate analysis by SBEM

2008

This paper deals with the thin bending plate analysis by using the symmetric approach of Boundary Element Method (SBEM). A formulation is used in which the plate boundary is discretized into boundary elements and is subjected to appropriate distributions of shear forces and couples, as well as of vertical displacement and rotations. These distributions are the causes and are modelled through appropriate shape functions, whereas the generalized effects are obtained, according to the Galerkin approach, as weighting of the displacements and the rotations, as well as of the shear forces and moments. In the equations system the algebraic operator is a symmetric matrix whose coefficients are defi…

bending plate SGBEM KirchoffSettore ICAR/08 - Scienza Delle Costruzioni
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