Finite Element Analysis of Nonlinear Structures

Mallett, R. H.; Marcal, Pedro V.

doi:10.1061/jsdeag.0002066

Cited by 123 publications

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“…For the core layer, the constitutive equation will be described in the next section. In order to define the stiffness matrix, the strain components in equation ( 17) are rewritten in terms of the shape functions and the element nodal displacement vector Q using equation (17) as:…”

Section: Finite Element Modeling Of Constrained Er Fluid Sandwich She...mentioning

confidence: 99%

“…The nonlinear amplitude dependent stiffness matrices in equations of motion have been expressed by two notations. In B-notation, according to the procedure developed by Mallet and Marcal [17], an asymmetric amplitude dependent stiffness matrix is achieved. However, Rajasekaran and Murray [18] showed that the derivation can be performed in such a way that a symmetric form of the nonlinear stiffness matrices in N-notation results.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear free vibration analysis of sandwich shell structures with a constrained electrorheological fluid layer

Mohammadi¹

2012

Smart Mater. Struct.

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Nonlinear vibration analysis of sandwich shell structures with a constrained electrorheological (ER) fluid is investigated for different boundary conditions. To accomplish this, a nonlinear finite element model of a multi-layer shell structure with an ER fluid layer in the core of the sandwich shell has been developed. A new notation referred to as H-notation is presented, in place of the two well known notations referred to as B-and N-notation, in order to represent the nonlinear equations of motion. This notation leads to a considerable reduction in the computational costs caused by the time-consuming integrations in the nonlinear vibration analysis of the structure using a direct iteration technique. In particular, this notation is very useful for solving the nonlinear vibration analysis of sandwich layered shell structures in which large numbers of integrations are required to be repeatedly performed throughout the direct iteration technique. Finally, for different boundary conditions, the effects of small and large displacements, core thickness ratio and electric field intensity on the nonlinear vibration damping behavior of the sandwich shell structure are presented.

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Section: Finite Element Modeling Of Constrained Er Fluid Sandwich She...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear free vibration analysis of sandwich shell structures with a constrained electrorheological fluid layer

Mohammadi¹

2012

Smart Mater. Struct.

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“…In the context of finite element solutions, Mallett & Marcal [10] proposed a scheme for writing the strain energy in a systematic way in 1968, known as 'appropriate form', containing three symmetric matrices-linear matrix, nonlinear matrices, and also expressed equilibrium and linear incremental equations using these matrices. In 1973, Rajasekaran & Murray [11] in their seminal paper presented an exact procedure/expression for deriving these matrices for various elements in an elegant manner.…”

Section: Main Achievements and Advances Of Researchmentioning

confidence: 99%

Review of the Nonlinear Vibration Analysis of Simply Supported Beams

Sun

2012

AMR

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The research of large amplitude vibration of simply supported beams can be dated back to 1950; many achievements and some evolution were accomplished by many researchers over hundred and fifty years. The development of nonlinear vibration formulations for beams has gone through distinct phases–earlier continuum solutions, development of appropriate forms, extra-variational simplifications, debate and discussions, variationally correct formulations and finally applications. A review of work in each of these phases is very necessary in order to have a complete understanding of the process of evolution of this field. This paper attempts to achieve precisely this objective.

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“…El uso de los métodos increméntales puso de relieve que se producía una acumulación de errores inadmisible por lo que se pasó a utilizar el método de Newton-Raphson tal y como hicieron Mallet y Marcal [MaM68] y Oden [Ode67]. Sin embargo el método de Newton-Raphson en su versión pura tiene un costo alto en cada iteración por lo que se utiliza el método de Newton Raphson modificado, cuasi-Newton y gradiente conjugado.…”

Section: Métodos Numéricosunclassified

Análisis del pandeo de pilares en régimen no lineal mediante splines generalizados

Sánchez¹

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2.7.2 Ecuaciones cr -£• del hormigón 72 2.7.3 Relaciones momento-curvatura 2.7.4 Diagrama trilineal momento-curvatura 2.7.5 Métodos de cálculo no lineal 2.7.6 Comprobación de elementos esbeltos 2.8 RESUMEN Y COMENTARIOS FINALES CAPÍTULO 3. SPLINES GENERALIZADOS 3.1 INTRODUCCIÓN 3.2 SPLINES GENERALIZADOS 3.2.1 Preliminares 3.2.2 Concepto de spline generalizado 3.3 FORMULACIÓN MATRICIAL DE LOS SPLINES GENERALIZADOS 3.3.1 Ecuación de equilibrio local del spline generalizado 3.3.2 Ejemplos de construcción de la ecuación de equilibrio local 3.3.3 Ecuación de equilibrio global del spline generalizado 3.3.4 Interpolación con splines generalizados 3.4 ANÁLISIS DE PROBLEMAS DE CONTORNO UNIDIMENSIONALES CON SPLINES GENERALIZADOS. SOLUCIÓN NODAL EXACTA Y ACCIONES REPARTIDAS EQUIVALENTES 3.4.1 Solución nodal exacta en problemas de contomo unidimensionales 3.4.2 Acciones repartidas equivalentes en problemas de contomo 3.4.3 Comentarios 3.5 APLICACIÓN AL ANÁLISIS DEL PANDEO DE PILARES EN RÉGIMEN LINEAL 3.5.1 Generalidades 3.5.2 Aplicación del concepto de acción repartida equivalente a la viga-columna 3.5.3 Ejemplo de aplicación CAPITULO 4. ANÁLISIS DEL PANDEO DE PILARES EN RÉGIMEN NO LINEAL MEDIANTE SPLINES GENERALIZADOS 4.1 INTRODUCCIÓN 4.2 MODELOS DISCRETOS PARA EL ESTUDIO DEL PANDEO DE PILARESEN RÉGIMEN NO LINEAL 4.2.1 Modelo con un grado de libertad 4.2.2 Modelo con varios grados de libertad 4.2.3 Ejemplo de ménsula con un grado de libertad 4.2.4 Ejemplo de ménsula con cuatro grados de libertad 4.2.5 Comentarios finales 4.3 PANDEO DE PILARES EN RÉGIMEN NO LINEAL EN EL CASO CONTINUO 4.3.1 Formulación del problema de pandeo en régimen no lineal 4.3.2 Discretización mediante elementos finitos 4.3.3 Comentarios sobre la no unicidad de solución del problema XII 4.4

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Finite Element Analysis of Nonlinear Structures

Cited by 123 publications

References 0 publications

Nonlinear free vibration analysis of sandwich shell structures with a constrained electrorheological fluid layer

Nonlinear free vibration analysis of sandwich shell structures with a constrained electrorheological fluid layer

Review of the Nonlinear Vibration Analysis of Simply Supported Beams

Análisis del pandeo de pilares en régimen no lineal mediante splines generalizados

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