Formulation and convergence of a mixed finite element method applied to elastic arches of arbitrary geometry and loading

Gellert, M.; Laursen, M.E.

doi:10.1016/0045-7825(76)90064-5

Cited by 20 publications

(9 citation statements)

References 11 publications

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“…Let us also mention the work of [13] for solving eigenvalue problems of circular arches and the one of [12] who propose a mixed finite element method.…”

Section: Introductionmentioning

confidence: 99%

Approximation of general arch problems by straight beam elements

Bernadou

Ducatel

1982

Numer. Math.

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“…Let us also mention the work of [13] for solving eigenvalue problems of circular arches and the one of [12] who propose a mixed finite element method.…”

Section: Introductionmentioning

confidence: 99%

Approximation of general arch problems by straight beam elements

Bernadou

Ducatel

1982

Numer. Math.

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“…(27), in addition to weighted average solutions in each element for equations (2 ! )- (24) and any prescribed slopes at the external boundaries, the following interelement boundary terms arc obtained: (33) Thus, whereas, by the same reasoning as before, interelement continuity of M , s and N?,, is ensured in thc limit, no similar wcighting is awarded to N,,s or u,,-thcrcby allowing, for cxample, the spurious solutions of Figure 9 to satisfy 611R = 0 for the arch of Figure 8…”

Section: (See Introduction) Tomentioning

confidence: 92%

The uniqueness characteristics of mixed finite element methods in linear elasticity

Boot

1987

Numerical Meth Engineering

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Having established the non-uniqueness, in general, of quadratic-linear functionals in elasticity, the investigative work on this topic is rcvicwcd, whence it is noted that thcrc is no existing formal approach for the identification of either the causes of singular solutions or suitable remedial measures that might ensure their elimination. A comparison of the weighted averages obtained from the single field and Keissner's principles is then used to identify a higher order uniqueness criterion for the latter. A detailed consideration of the application of the new condition to the arch equalions demonstrates how and why singular solutions can be obtained, and thence how suitable forms of remedial action can often be identified. Finally, several other classes of problem are briefly investigated in order to show how the criterion can be used to explain the full range of known behaviour of the mixed methods.

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“…Herrmann implemented one of the first mixed plate FEM using this RMVT and taking shear phenomenons into consideration (Herrmann, 1965(Herrmann, , 1967, quickly followed by other researchers (Bron and Dhatt, 1972;Chatterjee and Setlur, 1972). Over the last forty years, many mixed FEMs have been implemented for different theory such as 3D problems (Pian et al, 1983), elastic arches problems (Gellert and Laursen, 1976), Timoshenko's beams Belytschko, 1986a, 1986b) and of course particularly for plates Belytschko, 1986a, 1986b;Duan et al, 1999;de Miranda and Ubertini, 2006;Saleeb and Chang, 1987). Wriggers' book (Wriggers and Cartsensen, 2009) provides a wide range of application for mixed FEM.…”

Section: Introductionmentioning

confidence: 99%

Various double component mode synthesis and sub-structuring methods for dynamic mixed FEM

Garambois¹,

Besset²,

Jézéquel³

2015

European Journal of Mechanics - A/Solids

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International audienceMixed Finite Element Model Component Mode Synthesis (CMS) a b s t r a c t This paper presents various sub-structuring and component mode synthesis (CMS) reduction methods for dynamic mixed displacement-stress FEM. The idea is to imagine a new way of reducing a mixed FEM, by splitting the reduction of the displacement and the stress parameters and adapting primal existing modal reduction methods to each field of the mixed model. In this way, we can choose, for each sub-structure, different methods to truncate the displacements, the stresses and even the junction between the sub-structures. The results differ according to the combination of the methods used, and can show extremely promising results that significantly decrease the numerical size of the structures and still keep the benefits of the mixed method

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Formulation and convergence of a mixed finite element method applied to elastic arches of arbitrary geometry and loading

Cited by 20 publications

References 11 publications

Approximation of general arch problems by straight beam elements

Approximation of general arch problems by straight beam elements

The uniqueness characteristics of mixed finite element methods in linear elasticity

Various double component mode synthesis and sub-structuring methods for dynamic mixed FEM

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