Instability of Clamped-Hinged Circular Arches Subjected to a Point Load

DaDeppo, Donald A.; Schmidt, Robert

doi:10.1115/1.3423734

Cited by 87 publications

(39 citation statements)

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“…4a. Different numbers of the 4-noded elements were tried, and only six elements were enough to obtain good results: see Table 5 (the classical solution was contributed by DaDeppo and Schmidt, 1975).…”

Section: Numerical Examplesmentioning

confidence: 99%

A formulation and implementation of geometrically exact curved beam elements incorporating finite strains and finite rotations

Kapania¹,

Li²

2003

Computational Mechanics

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This paper deals with the formulation and implementation of the curved beam elements based on the geometrically exact curved/twisted beam theory assuming that the beam cross-section remains rigid. The summarized beam theory is used for the slender beams or rods. Along with the beam theory, some basic concepts associated with finite rotations and their parametrizations are briefly summarized. In terms of a non-vectorial parametrization of finite rotations under spatial descriptions, a formulation is given for the virtual work equations that leads to the load residual and tangential stiffness operators. Taking the advantage of the simplicity in formulation and clear classical meanings of both rotations and moments, the non-vectorial parametrization is applied to implement a four-noded 3-D curved beam element, in which the compound rotation is represented by the unit quaternion and the incremental rotation is parametrized using the incremental rotation vector. Only static problems are considered. Conventional Lagrangian interpolation functions are adopted to approximate both the reference curve and incremental rotation of the deformed beam. Reduced integration is used to overcome locking problems. The finite element equations are developed for static structural analyses, including deformations, stress resultants/couples, and linearized/nonlinear bifurcation buckling, as well as post-buckling analyses of arches subjected to different types of loads, such as self-weight, snow, and pressure (wind) loads. Several examples are used to test the formulation and its Fortran implementation.

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Section: Numerical Examplesmentioning

confidence: 99%

A formulation and implementation of geometrically exact curved beam elements incorporating finite strains and finite rotations

Kapania¹,

Li²

2003

Computational Mechanics

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“…The present 20 element discretization exhibits a slightly lower buckling load but still captures the overall behavior. The buckling load for the 40 element discretization has been found to 884, which is within an error of 1:5% of the value reported by da Deppo and Schmidt [36] of 897. A better accuracy for the 20 element discretization could be obtained with the present formulation by including pre-curvature as in [7].…”

Section: Buckling Of Clamped-hinged Circular Archmentioning

confidence: 74%

“…A nonlinear analysis of the pre-buckling and post-buckling behavior of the clamped-hinged circular arch illustrated in Figure 8 [35], Ibrahimbegovic [7], and Gerstmayr and Irschik [31]. Furthermore, inextendable elastica solutions for post-buckling of arches with various angles have been presented by DaDeppo and Schmidt [36]. Parameters similar to those in [7] have been used corresponding to an arch with radius R D 100 and an angle of D 215…”

Section: Buckling Of Clamped-hinged Circular Archmentioning

confidence: 99%

Explicit free‐floating beam element

Nielsen

Krenk

2014

Numerical Meth Engineering

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SUMMARYA two-node free-floating beam element capable of undergoing arbitrary large displacements and finite rotations is presented in explicit form. The configuration of the beam in three-dimensional space is represented by the global components of the position of the beam nodes and an associated set of convected base vectors (directors). The local constitutive stiffness is derived from the complementary energy of a set of six independent deformation modes, each corresponding to an equilibrium state of constant internal force or moment. The deformation modes are characterized by generalized strains, formed via scalar products of the element related vectors. This leads to a homogeneous quadratic strain definition in terms of the generalized displacements, whereby the elastic energy becomes at most bi-quadratic. Additionally, the use of independent equilibrium modes to set up the element stiffness avoids interpolation of kinematic variables, resulting in a locking-free formulation in terms of three explicit matrices. A set of classic benchmark examples illustrates excellent performance of the explicit beam element.

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“…. are of size 9 × 9 and are formed only once and hence both the secant stiffness and tangent stiffness matrices are formed by varying the scalar multiples in Equations (17) and (18). Hence, a little increase in the computation effort of these matrices is offset by the gain in computing them only once.…”

Section: Variable Order Secant Matrices For the Kinematically Exact Rmentioning

confidence: 99%

Variable order secant matrix technique applied to the elastic postbuckling of arches

Jayachandran

White

2007

Commun. Numer. Meth. Engng.

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SUMMARYThis paper presents the implementation of Reissner's (J. Appl. Math. Phys. 1972; 23:795-804) straindisplacement relations for a planar beam using a variable order secant matrix (VOSM) technique. The secant matrices are formed using a Taylor expansion of the strain energy and hence the order of the secant and tangent matrices to be included in the nonlinear analysis can be varied depending upon the degree of nonlinearity involved in the problem. Nevertheless, a maximum of 24 matrices is sufficient to obtain predicted internal stress resultants to within 0.2% of the converged solution in all the problems tested. Using a three-noded isoparametric beam element, the accuracy of the VOSM method is demonstrated for the elastic postbuckling of arches.

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Instability of Clamped-Hinged Circular Arches Subjected to a Point Load

Cited by 87 publications

References 0 publications

A formulation and implementation of geometrically exact curved beam elements incorporating finite strains and finite rotations

A formulation and implementation of geometrically exact curved beam elements incorporating finite strains and finite rotations

Explicit free‐floating beam element

Variable order secant matrix technique applied to the elastic postbuckling of arches

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