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

2017 ◽  
Vol 14 (5) ◽  
pp. 765-804 ◽  
Author(s):  
Jun-Bin Huang ◽  
Song Cen ◽  
Yan Shang ◽  
Chen-Feng Li
Keyword(s):  
Free Vibration ◽  
Displacement Function ◽  
Reissner Plate ◽  
Function Element

scholarly journals Some advances in high-performance finite element methods

2019 ◽  
Vol 36 (8) ◽  
pp. 2811-2834 ◽  
Author(s):  
Song Cen ◽  
Cheng Jin Wu ◽  
Zhi Li ◽  
Yan Shang ◽  
Chenfeng Li
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
High Performance ◽  
Displacement Function ◽  
Content Type ◽  
Reissner Plate ◽  
Long Time ◽  
History Of ◽  
Function Element ◽  
Element Method

Purpose The purpose of this paper is to give a review on the newest developments of high-performance finite element methods (FEMs), and exhibit the recent contributions achieved by the authors’ group, especially showing some breakthroughs against inherent difficulties existing in the traditional FEM for a long time. Design/methodology/approach Three kinds of new FEMs are emphasized and introduced, including the hybrid stress-function element method, the hybrid displacement-function element method for Mindlin–Reissner plate and the improved unsymmetric FEM. The distinguished feature of these three methods is that they all apply the fundamental analytical solutions of elasticity expressed in different coordinates as their trial functions. Findings The new FEMs show advantages from both analytical and numerical approaches. All the models exhibit outstanding capacity for resisting various severe mesh distortions, and even perform well when other models cannot work. Some difficulties in the history of FEM are also broken through, such as the limitations defined by MacNeal’s theorem and the edge-effect problems of Mindlin–Reissner plate. Originality/value These contributions possess high value for solving the difficulties in engineering computations, and promote the progress of FEM.

scholarly journals L-P Perturbation Solution of Nonlinear Free Vibration of Prestressed Orthotropic Membrane in Large Amplitude

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Liu Chang-jiang ◽  
Zheng Zhou-lian ◽  
He Xiao-ting ◽  
Sun Jun-yi ◽  
Song Wei-ju ◽  
...  
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Lateral Displacement ◽  
Membrane Surface ◽  
Displacement Function ◽  
Governing Equations ◽  
Membrane Structures ◽  
Nonlinear Free Vibration ◽  
Time Curve ◽  
Computational Basis

This paper reviewed the research on the nonlinear free vibration of pre-stressed orthotropic membrane, which is commonly applied in building membrane structures. We applied the L-P perturbation method to solve the governing equations of large amplitude nonlinear free vibration of rectangular orthotropic membranes and obtained a simple approximate analytical solution of the frequency and displacement function of large amplitude nonlinear free vibration of rectangular membrane with four edges simply supported. By giving computational examples, we compared and analyzed the frequency results. In addition, vibration mode of the membrane and displacement and time curve of each feature point on the membrane surface were analyzed in the computational example. Results obtained from this paper provide a simple and convenient method to calculate the frequency and lateral displacement of nonlinear free vibration of rectangular orthotropic membranes in large amplitude. Meanwhile, the results provide some theoretical basis for solving the response of membrane structures under dynamic loads and provide some computational basis for the vibration control and dynamic design of building membrane structures.

scholarly journals A Unified Solution for the Vibration Analysis of Lattice Sandwich Beams with General Elastic Supports

2021 ◽  
Vol 11 (19) ◽  
pp. 9141
Author(s):  
Yeqing Jin ◽  
Ruiping Yang ◽  
Hengxu Liu ◽  
Haiwei Xu ◽  
Hailong Chen
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Present Method ◽  
Displacement Function ◽  
Vibration Characteristics ◽  
Homogeneous Layer ◽  
Sandwich Beams ◽  
Arbitrary Boundary ◽  
Elastic Supports ◽  
Various Boundary Conditions

Free vibration analyses of lattice sandwich beams with general elastic supports have rarely been discussed in this field’s literature. In this paper, a unified method is proposed to study the free vibration characteristics of lattice sandwich beams under various boundary conditions. The proposed method is to convert the three truss cores of lattice sandwich beams into an equivalent homogeneous layer and introduce two different types of constraint springs to simulate the general elastic support boundary at both ends of lattice sandwich beams. By changing the rigidity of the boundary restraint spring, various boundary conditions can be easily obtained without modifying the solving algorithm and solving process. In order to overcome all the discontinuities or jumps associated with the elastic boundary support conditions, the displacement function of lattice sandwich beams is usually obtained as an improved Fourier cosine series along with four sine terms. On this basis, the unknown series coefficients of the displacement function are treated as the generalized coordinates and solved using the Rayleigh–Ritz method. The correctness of the present method is verified through comparison with existing literature. The calculation results of the present method are highly accurate, indicating that the present method is suitable for analyzing the vibration characteristics of lattice sandwich beams with general elastic supports. In addition, the effects of beam length, panel thickness, core height, radius and truss inclination on the natural frequencies of lattice sandwich beams with arbitrary boundary conditions have been discussed in this paper.

scholarly journals Distortion-resistant and locking-free eight-node elements effectively capturing the edge effects of Mindlin–Reissner plates

2017 ◽  
Vol 34 (2) ◽  
pp. 548-586 ◽  
Author(s):  
Yi Bao ◽  
Song Cen ◽  
Chenfeng Li
Keyword(s):  
Edge Effects ◽  
Displacement Function ◽  
High Order ◽  
Plate Bending ◽  
Free Boundaries ◽  
Content Type ◽  
Patch Tests ◽  
Quadrilateral Plate ◽  
Plate Elements ◽  
Function Element

Purpose A simple shape-free high-order hybrid displacement function element method is presented for precise bending analyses of Mindlin–Reissner plates. Three distortion-resistant and locking-free eight-node plate elements are proposed by utilizing this method. Design/methodology/approach This method is based on the principle of minimum complementary energy, in which the trial functions for resultant fields are derived from two displacement functions, F and f, and satisfy all governing equations. Meanwhile, the element boundary displacements are determined by the locking-free arbitrary order Timoshenko’s beam functions. Then, three locking-free eight-node, 24-DOF quadrilateral plate-bending elements are formulated: HDF-P8-23β for general cases, HDF-P8-SS1 for edge effects along soft simply supported (SS1) boundary and HDF-P8-FREE for edge effects along free boundary. Findings The proposed elements can pass all patch tests, exhibit excellent convergence and possess superior precision when compared to all other existing eight-node models, and can still provide good and stable results even when extremely coarse and distorted meshes are used. They can also effectively solve the edge effect by accurately capturing the peak value and the dramatical variations of resultants near the SS1 and free boundaries. The proposed eight-node models possess potential in engineering applications and can be easily integrated into commercial software. Originality/value This work presents a new scheme, which can take the advantages of both analytical and discrete methods, to develop high-order mesh distortion-resistant Mindlin–Reissner plate-bending elements.

scholarly journals A Unified Formulation for Free Vibration of Spherical Cap Based on the Ritz Method

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Yuan Du ◽  
Liping Sun ◽  
Xuhong Miao ◽  
Fuzhen Pang ◽  
Haichao Li ◽  
...  
Keyword(s):  
Free Vibration ◽  
Jacobi Polynomials ◽  
Domain Decomposition Method ◽  
Ritz Method ◽  
Axial Direction ◽  
Displacement Function ◽  
Spherical Cap ◽  
Simple Boundary ◽  
Edge Conditions ◽  
Adjacent Segments

The free vibration characteristic of spherical cap with general edge constraints is studied by means of a unified method. The energy method and Kirchhoff hypothesis are adopted to derive the formulas. The displacement functions are improved based on the domain decomposition method, in which the unified Jacobi polynomials are introduced to represent the displacement function component along circumferential direction. The displacement function component along axial direction is still the Fourier series. In addition, the spring stiffness method forms a unified format to deal with various complex boundary conditions and the continuity conditions at two adjacent segments. Then, the final solutions can be obtained based on the Ritz method. To prove the validity of this method, the results of the same condition are compared with FEM, published literatures, and experiment. The results show that the present method has the advantages of fast convergence, high solution accuracy, simple boundary simulation, etc. In addition, some numerical results of uniform and stepped spherical caps with various geometric parameters and edge conditions are reported.

scholarly journals Influence of different material parameters on nonlinear vibration of the cylindrical skeleton supported prestressed fabric composite membrane

2021 ◽  
Vol 60 (1) ◽  
pp. 190-206
Author(s):  
Changjiang Liu ◽  
Mengfei Wang ◽  
Zhoulian Zheng ◽  
Jian Liu ◽  
Haibing Xie ◽  
...  
Keyword(s):  
Free Vibration ◽  
Composite Membrane ◽  
Displacement Function ◽  
Frequency Function ◽  
Width Ratio ◽  
Kutta Method ◽  
Material Parameters ◽  
Runge Kutta Method ◽  
Fabric Composite ◽  
Runge Kutta

Abstract In order to study the influence of geometric nonlinearity and material parameters on the free vibration behavior of the cylindrical skeleton supported prestressed fabric composite membrane. In this paper, based on von Karman's large deflection theory and D’Alembert's principle, the governing equations of nonlinear viscous damped prestressed free vibration of frame supported anisotropic membrane structures were established. By using Galerkin and KBM perturbation method, the analytical expressions of frequency function, displacement function and mode shape of nonlinear free vibration were obtained. In order to verify the effectiveness and effective range of the method, the fourth order Runge-Kutta method was used for numerical calculation. The calculation examples of membrane material parameters were given. The calculation and analysis of different membrane prestress, different length width ratio, different rise span ratio and different material parameters (elastic modulus ratio, viscous damping and material density) were carried out. The results were compared with the numerical results obtained by Runge-Kutta method to verify the accuracy of the method. The research results of this paper provide a theoretical reference for the selection of membrane materials, the subsequent calculation of wind-induced stability of steel skeleton membrane structure and the design of wind-driven rain resistance.

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