Derivation of element stiffness matrices by assumed stress distributions

Pian, T. H. H.

doi:10.2514/3.2546

Cited by 661 publications

(260 citation statements)

References 4 publications

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“…It should be noted that the strain energy of a finite element developed through a hybrid method may be an upper-or lowerbound, however it is always bounded by that of a compatible model using the same type of inter-element boundary displacements and that of an equilibrium model using the same type of interior stresses [18].…”

Section: Mesh Refinement and Bounding Of The Solutionmentioning

confidence: 99%

Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications

Almeida

Correia

Pinho

2015

Engineering Structures

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a b s t r a c tThe specific features of the proposed force-based formulation derived in the companion paper, which is applied for the first time to higher-order beam theories, are herein thoroughly validated. Introductory numerical examples illustrate the influence of mesh refinement, boundary conditions, and slenderness ratios for isotropic linear elastic response. Specific higher-order effects-unique to the developed element-are then suitably interpreted, as well as the formulation appropriateness to consider distributed loads and to model three-dimensional behaviour, which is verified with solid finite element analyses. Extensive comparisons against existing proposals, namely other refined higher-order beam theories, emphasize the performance of the proposed approach. Finally, the nonlinear response of the element with a multiaxial J2 linear plasticity material model is analysed, highlighting its advantages in relation to a classical force-based Euler-Bernoulli beam using a one-dimensional plastic material model with kinematic hardening.

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Section: Mesh Refinement and Bounding Of The Solutionmentioning

confidence: 99%

Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications

Almeida

Correia

Pinho

2015

Engineering Structures

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“…Using Voigt notation, the vector form of the Green-Lagrange strain tensor is defined as (9) The work conjugate stress measure of the Green-Lagrange strain tensor is the second Piola-Kirchhoff stress tensor, , that can be expressed in vector form using Voigt notation as ,…”

Section: General Geometric and Materials Nonlinear Theory Including Shmentioning

confidence: 99%

“…A large body of research has been devoted to mixed finite element formulations since they were first introduced in the pioneering work of Pian [9]. Several finite elements based on different variational principles have been developed [10][11][12][13][14] and relationships among them have been established [15,16].…”

Section: Introductionmentioning

confidence: 99%

Finite element response sensitivity analysis using three‐field mixed formulation: general theory and application to frame structures

Barbato

Zona

Conte

2006

Numerical Meth Engineering

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SUMMARYThis paper presents a method to compute response sensitivities of finite element models of structures based on a three-field mixed formulation. The methodology is based on the Direct Differentiation Method (DDM), and produces the response sensitivities consistent with the numerical finite element response. The general formulation is specialized to frame finite elements and details related to a newly developed steelconcrete composite frame element are provided. DDM sensitivity results are validated through the forward Finite Difference Method (FDM) using a finite element model of a realistic steel-concrete composite frame subjected to quasi-static and dynamic loading. The finite element model of the structure considered is constructed using both monolithic frame elements and composite frame elements with deformable shear connection based on the three-field mixed formulation. The addition of the analytical sensitivity computation algorithm presented in this paper extends the use of finite elements based on a three-field mixed formulation to applications that require finite element response sensitivities. Such applications include structural reliability analysis, structural optimization, structural identification, and finite element model updating.KEY WORDS: Hu-Washizu functional; three-field mixed finite element formulation; material constitutive parameters; finite element response sensitivity; steel-concrete composite beam.

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“…However relatively less attention has been addressed to the development of layer-wise based FE for interlaminar free-edge stresses analysis. Most of layer-wise FEs developed for free edge analysis [28][29][30] are based on the hybrid stress concept using the variational principle of Pian [31].…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Finite element analysis of free-edge stresses in composite laminates under mechanical an thermal loading

Nguyen

Caron²

2009

Composites Science and Technology

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To cite this version:Viet-Tung Nguyen, Jean-François Caron. Finite element analysis of free-edge stresses in composite laminates under mechanical an thermal loading. Composites Science and Technology, Elsevier, 2009, 69 (1), pp.40. <10.1016/j.compscitech.2007.10.055>. F i n i t e e l e m e n t a n a l y s i s o f f r e e -e d g e s t r e s s e s i n c o m p o s i t e l a m i n a t e s u n d e r m e -c h a n i c a l a n t h e r m a l l o a d i n g V i e t -T u n g N g u y e n , J e a n -F r a n c o i s C a r o n P I I : S 0 2 6 Accepted Manuscript ACCEPTED MANUSCRIPTFinite element analysis of free-edge stresses in

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Derivation of element stiffness matrices by assumed stress distributions

Cited by 661 publications

References 4 publications

Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications

Force-based higher-order beam element with flexural-shear-torsional interaction in 3D frames. Part II: Applications

Finite element response sensitivity analysis using three‐field mixed formulation: general theory and application to frame structures

Finite element analysis of free-edge stresses in composite laminates under mechanical an thermal loading

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