Hybrid stress and analytical functions for analysis of thin plates bending

Rezaiee‐Pajand, Mohammad; Karkon, Mohammad

doi:10.1590/s1679-78252014000400001

Cited by 5 publications

(2 citation statements)

References 29 publications

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“…THS: A triangular hybrid stress element based on analytical solutions of thin plate equations proposed by Rezaiee-Pajand et al (2014). ARS-T9: A triangular Mindlin plate element based on the improved shear strain interpolation derived from the locking-free Timoshenko's beam element proposed by Soh et al (1999).…”

Section: Numerical Examplesmentioning

confidence: 99%

A New Triangular Hybrid Displacement Function Element for Static and Free Vibration Analyses of Mindlin-Reissner Plate

Huang

Cen

Shang

et al. 2017

Lat. Am. j. solids struct.

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A new 3-node triangular hybrid displacement function Mindlin-Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko's beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses.

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Section: Numerical Examplesmentioning

confidence: 99%

A New Triangular Hybrid Displacement Function Element for Static and Free Vibration Analyses of Mindlin-Reissner Plate

Huang

Cen

Shang

et al. 2017

Lat. Am. j. solids struct.

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“…are revealed. Aiming at improving accuracy and efficiency, many hybrid stress element methods (Rah et al , 2011; Wang and Qin, 2011; Rah et al , 2013; Ma and Chen, 2013; Rezaiee-Pajanda and Karkonb, 2014; Ma and Chen, 2014) have been proposed, showing good properties. On the basis of the assumed hybrid approach, Tian et al (2001) etc.…”

Section: Introductionmentioning

confidence: 99%

A novel hybrid stress meshless method for two-dimension elastic structure with a traction-free circular boundary

Cao

Guan

Chen

2017

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Purpose To increase the use of the meshless method, a hybrid stress method is introduced into the meshless method. Design/methodology/approach The method is based on the radial point interpolation method (RPIM). According to the Hellinger Reissner principle, stress functions are introduced into the solution procedure. Finite elements are used as background cells for integration. All cells are divided into two types – the H cells, which are around the traction-free circular boundary, and the G cells. For the H cells, stress functions in polar coordinates are created. For the G cells, 12-parameter stress functions in Cartesian coordinates are used. Stress functions are based on equilibrium equations and stress compatible equation. Findings Numerical results show that this method is reliable. Originality/value Hybrid stress methods have been applied to finite element methods, but the finite element methods have not been applied into meshless methods.

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