The Equilibrium Finite Elements in Computation of Elastic Structures

Kalanta, Stanislovas

doi:10.1080/13921525.1995.10531500

Cited by 11 publications

(5 citation statements)

References 4 publications

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“…Discretization of the structure, which geometry, materials and cross-sectional parameters are known, in this work is performed using a equilibrium finite elements method [12,20,23]. By using this method equilibrium equations are written more accurately compared with other types of finite elements.…”

Section: Discretization Of the Structurementioning

confidence: 99%

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Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion

Alawdin¹,

Atkočiūnas²,

Liepa³

2016

Civil and Environmental Engineering Reports

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Paper focuses on the problems of application of extreme energy principles and nonlinear mathematical programing in the theory of structural shakedown. By means of energy principles, which describes the true stress-strain state conditions of the structure, the dual mathematical models of analysis problems are formed (static and kinematic formulations). It is shown how common mathematical model of the structures optimization at shakedown with safety and serviceability constraints (according to the ultimate limit state (ULS) and serviceability limit state (SLS) requirements) on the basis of previously mentioned mathematical models is formed. The possibilities of optimization problem solution in the context of physical interpretation of optimality criterion of Rosen’s algorithm are analyzed.

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Section: Discretization Of the Structurementioning

confidence: 99%

“…are not identically satisfied. Therefore equilibrium of the discrete model are ensured for the elements of the structure and for their main nodes [23]. By putting expression (26) into equations (27)…”

Section: Discretization Of the Structurementioning

confidence: 99%

Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion

Alawdin¹,

Atkočiūnas²,

Liepa³

2016

Civil and Environmental Engineering Reports

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“…The equilibrium equation matrix [A] could be formulated from the coefficients of the equilibrium equations of nodes and elements or from the formula [A] = [C ] T Ā [19]; here the compatibility matrix [C ] describing the relation between global displacements of the structural nodes and nodal displacements of elements; Ā = diag [A k ] is the quasi-diagonal matrix, whose diagonal submatrices are composed from the coefficients of the static equations …”

Section: Formulation Of the Main Dependenciesmentioning

confidence: 99%

“…, r joined in the nodes. The dependencies of the model (1) can be composed by using the equilibrium finite element method [19], and the model (3) can be created with the help of the equilibrium or geometrically compatible finite element method [20], because the stiffness matrix K can be formulated not only from the indicated formula, but also from the stiffness matrices of elements too.…”

Section: Formulation Of the Main Dependenciesmentioning

confidence: 99%

Discrete optimization problems of the steel bar structures

Kalanta

Atkočiūnas

Venskus

2009

Engineering Structures

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“…Steel structures will be modelled by the equilibrium finite elements with interpolation functions of internal forces (De Veubeke 1963;Gallagher 1975;Kalanta 1995;Wilson 2002). LINK11 and BEAM31 types of finite elements are described in this paper.…”

Section: Beam Finite Elements: Yield and Strength Conditionsmentioning

confidence: 99%

Saosys Toolbox as Matlab Implementation in the Elastic‐plastic Analysis and Optimal Design of Steel Frame Structures

Jankovski

Atkočiūnas

2010

Journal of Civil Engineering and Management

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Abstract. The improved mathematical model of steel frame structures' design is created. The loading is simple, and plastic strains are evaluated. Energy principles of deformable body mechanics and mathematical programming theory are employed. Equilibrium finite elements with interpolation functions of internal forces are used for discretization. The elements are designed using HE, IPE, RHS steel profile assortments and considering dispersion of geometrical characteristics of profile assortment sets. Optimal design of steel structures is realized by using the experimental tool system JWM SAOSYS Toolbox v0.42, which was created by the authors in MATLAB environment. SAOSYS architecture operates with objectoriented finite elements pseudo-polymorphously. The possibilities of this system are demonstrated by considering a numerical example of optimal design of industrial building frame with strength and stiffness constraints. The assumption of small displacements is adopted for computations.

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The Equilibrium Finite Elements in Computation of Elastic Structures

Cited by 11 publications

References 4 publications

Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion

Optimization of the Structures at Shakedown and Rosen’s Optimality Criterion

Discrete optimization problems of the steel bar structures

Saosys Toolbox as Matlab Implementation in the Elastic‐plastic Analysis and Optimal Design of Steel Frame Structures

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