Finite Element Procedures in Engineering Analysis

Bathe, Klaus‐Jürgen; Saunders, H.

doi:10.1115/1.3264375

Cited by 839 publications

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“…For every 0 and i¡ belonging to [H0(Q)]2 the bilinear form a has the following expression: and the theory of [3] give the existence and uniqueness of the solution and the following a priori estimate:…”

Section: Notationsmentioning

confidence: 99%

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Uniform interior error estimates for the Reissner-Mindlin plate model

Gastaldi¹

1993

Math. Comp.

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Abstract. Interior error estimates are derived for the solution of the ReissnerMindlin plate model discretized by mixed-interpolated elements. Precisely, it is shown that the error in an interior domain can be estimated by the sum of two terms: the first has the best order of accuracy that is possible locally for the finite element spaces used, the second is a weak norm of the error on a slightly larger domain (this term measures the effects from outside of this domain). The analysis is based on some abstract properties enjoyed by the finite element spaces considered.

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Section: Notationsmentioning

confidence: 99%

“…Moreover, note that the load has been scaled so that the solution tends to a nonzero limit as / tends to zero. See for instance [3] for more details. We consider the finite element approximation of the Reissner-Mindlin plate proposed recently in [6].…”

Section: Introductionmentioning

confidence: 99%

Uniform interior error estimates for the Reissner-Mindlin plate model

Gastaldi¹

1993

Math. Comp.

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“…Information for structural engineers covering the complete field of finite element analysis in solid mechanics is listed, e.g. (Bathe 1982;Němec et al 2010). Let us describe some aspects of the geometrical non-linear analysis that was applied.…”

Section: Geometrical Non-linear Analysismentioning

confidence: 99%

Geometrically Non-Linear Finite Element Reliability Analysis of Steel Plane Frames With Initial Imperfections / Plieninių Rėmų Su Defektais Geometriškai Netiesinė Baigtinių Elementų Patikimumo Analizė

Kala

2012

Journal of Civil Engineering and Management

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Abstract. The random load carrying capacity of steel plane frames with bracing stiffness is studied. The load carrying capacity is evaluated using the geometrically non-linear FEM analysis. The incremental stiffness matrix of a slightly curved element utilized in the non-linear incremental analysis is listed. Initial imperfections are considered as random variables. Statistical analysis and Sobol sensitivity analysis are performed using the Latin Hypercube Sampling method. The effect of initial random imperfections on the load carrying capacity is studied, whilst assuming constant slenderness of the columns. The evaluation parameters are the pair of non-random values of elastic bracing stiffness, and system length of the columns. The paper illustrates that the load carrying capacity is very sensitive to initial crookedness of the columns in the event that the non-sway (symmetric) and sway (anti-symmetric) buckling modes coincide. In this case, the design load carrying capacity obtained from statistical analysis according to the EN 1990the EN (2002 standard is relatively very small (of low safety). Results show that the reliability of design of a steel frame according to EUROCODE 3 (1993) is significantly misaligned. The significance of the first and the second buckling forces as indicators of sensitivity of the load carrying capacity to the imperfections is discussed.

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“…Second degree serendipity shape functions were used to interpolate the displacement ®eld within an element [22].…”

Section: Numerical Modelmentioning

confidence: 99%

Combined numerical–experimental model for the identification of mechanical properties of laminated structures

Araújo

Soares²,

Freitas³

et al. 2000

Composite Structures

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A combined numerical±experimental method for the identi®cation of six elastic material modulus of generally thick composite plates is proposed in this paper. This technique can be used in composite plates made of di erent materials and with general stacking sequences. It makes use of experimental plate response data, corresponding numerical predictions and optimisation techniques. The plate response is a set of natural frequencies of¯exural vibration. The numerical model is based on the ®nite element method using a higher-order displacement ®eld. The model is applied to the identi®cation of the elastic modulus of the plate specimen through optimisation techniques, using analytical sensitivities. The validity, e ciency and potentiality of the proposed technique is discussed through test cases. Ó

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Finite Element Procedures in Engineering Analysis

Cited by 839 publications

References 0 publications

Uniform interior error estimates for the Reissner-Mindlin plate model

Uniform interior error estimates for the Reissner-Mindlin plate model

Geometrically Non-Linear Finite Element Reliability Analysis of Steel Plane Frames With Initial Imperfections / Plieninių Rėmų Su Defektais Geometriškai Netiesinė Baigtinių Elementų Patikimumo Analizė

Combined numerical–experimental model for the identification of mechanical properties of laminated structures

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