Method of matched sections as a beam-like approach for plate analysis

Orynyak, Igor; Danylenko, Kirill

doi:10.1016/j.finel.2023.104103

Cited by 3 publications

(4 citation statements)

References 29 publications

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“…Now it is easy to formulate the general algorithm of solution, which is identical to this one proposed in our works [24], [25] except the number of main parameters of the problem (number of unknowns). So, repeat it in short.…”

Section: Algorithm Of Solutionmentioning

confidence: 99%

“…So, the number of equations and number of unknowns does coincide, and algorithm of solution reduces to a) proper meshing the structure; b) proper organization of bypass through the structure and numbering the elements; c) proper numbering the unknowns; d) compilation and solution of the matrix equation; e) presentation of results inside each element. All these essential steps were explained in our works [24], [25].…”

Section: Algorithm Of Solutionmentioning

confidence: 99%

“…The main idea of works [24], [25] is that solution within small 2D rectangular element can be presented as combination of two separate 1D problems, each of them is dependent only from one coordinate x or y . Two separate problems are united by continuity condition in the middle of element.…”

Section: Introductionmentioning

confidence: 99%

“…Two separate problems are united by continuity condition in the middle of element. For 2D plate deformation the solutions with respect of any coordinate axis closely resemble that for 1D beam problem, so we titled our method [24] as a "beamlike approach". Here for the temperature task, there is no beam analogy, but the essence of the method remains the same: we attribute two sets of physical unknowns (temperature, T and heat flux, Q) at the middle of each side and consider that these values are functions of only one coordinate axis which is directed normally to the side considered.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Implicit direct time integration of the heat conduction problem in the Method of Matched Sections

Orynyak,

Tsybulnyk,

Danylenko

et al. 2024

Mech. Adv. Technol.

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The paper is devoted to further elaboration of the Method of Matched Sections as a new branch of finite element method in application to the transient 2D temperature problem. The main distinction of MMS from conventional FEM consist in that the conjugation is provided between the adjacent sections rather than in the nodes of the elements. Important feature is that method is based on approximate strong form solution of the governing differential equations called here as the Connection equations. It is assumed that for each small rectangular element the 2D problem can be considered as the combination of two 1D problems – one is x-dependent, and another is y-dependent. Each problem is characterized by two functions – the temperature, , and heat flux . In practical realization for rectangular finite elements the method is reduced to determination of eight unknowns for each element – two unknowns on each side, which are related by the Connection equations, and requirement of the temperature continuity at the center of element. Another salient feature of the paper is an implementation of the original implicit time integration scheme, where the time step became the parameter of shape function within the element, i.e. it determines the behavior of the Connection equations. This method was early proposed by first author for number of 1D problem, and here in first time it is applied for 2D problems. The number of tests for rectangular plate exhibits the remarkable properties of this “embedded” time integration scheme with respect to stability, accuracy, and absence of any restrictions as to increasing of the time step.

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Section: Algorithm Of Solutionmentioning

confidence: 99%

Section: Algorithm Of Solutionmentioning

confidence: 99%