Implementation of a direct procedure for critical point computations using preconditioned iterative solvers

Kouhia, Reijo; Tma, Miroslav; Mäkinen, Jari; Fedoroff, Alexis; Marjamäki, Heikki

doi:10.1016/j.compstruc.2012.02.009

Cited by 8 publications

(4 citation statements)

References 56 publications

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“…A small perturbation moment of 1 N⋅m is applied at the beam top-end to make the detection of the critical points easier, as shown in Figure 6(a). The equilibrium paths obtained with the presented method by using ∈ [2,4,8,16] elements are shown, respectively, in Figure 7, where the meaning of legends is defined by Figure 6(b).…”

Section: Tangent Stiffness Matricesmentioning

confidence: 99%

“…The load case is shown in Figure 8, where the node is under a vertical load along the negative -axis direction. By using ∈ [2,4,8,16] elements for each member, the equilibrium paths of node obtained by the presented method are shown, respectively, in Figure 9.…”

Section: -Member Hexagonal Star-shaped Shallow Domementioning

confidence: 99%

“…In the direct method, the equilibrium equations are augmented with a criticality condition [2,3]. Since the augmented equations are highly nonlinear, a nice preconditioner [4] is essential for the successful application of the method. In the indirect method, the behavior of the structure is monitored by following the equilibrium path and detecting the singularity of the tangent stiffness matrix associated with each point on the path.…”

Section: Introductionmentioning

confidence: 99%

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Identifying Critical Loads of Frame Structures with Equilibrium Equations in Rate Form

Zai-kang

Kong

Wang

2015

Mathematical Problems in Engineering

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Frame structures are widely used in engineering practice. They are likely to lose their stability before damage. As an indicator of load-carrying capability, the first critical load plays a crucial role in the design of such structures. In this paper, a new method of identifying this critical load is presented, based on the governing equations in rate form. With the presented method, a great deal of well-developed numerical methods for ordinary differential equations can be used. As accurate structural tangent stiffness matrices are essential to stability analysis, the method to obtain them systematically is discussed. To improve the computational efficiency of nonlinear stability analysis in large-scale frame structures, the corotational substructure elements are formulated as well to reduce the dimension of the governing equations. Four examples are studied to illustrate the validity and efficiency of the presented method.

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Section: Tangent Stiffness Matricesmentioning

confidence: 99%

Section: -Member Hexagonal Star-shaped Shallow Domementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Identifying Critical Loads of Frame Structures with Equilibrium Equations in Rate Form

Zai-kang

Kong

Wang

2015

Mathematical Problems in Engineering

View full text Add to dashboard Cite

show abstract

“…Generally, the critical points are detected by two approaches called direct and indirect methods [2]. In the direct method, the critical points are determined by solving the algebraic equilibrium equations and a criticality condition [3][4][5][6]. In the indirect method, the critical points are identified by following the equilibrium path continually and combining the detection of the singularity of tangent stiffness matrices [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%