Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix

In this analytical study, free vibration analyses of a 3d mixed formulation beam element are performed by adopting force-based consistent mass matrix that incorporates shear and rotary inertia effects. The force-based approach takes into account the actual distribution of mass of an element in the derivation of the mass matrix. Moreover, the force-based approach enables accurate determination of free vibration frequencies of members with varying geometry and material distribution without any need for specification of different displacement shape functions for each individual case. This phenomenon is justified by comparing free vibration frequencies of cantilever beams that have circular and rectangular cross-sections and various mass distribution configurations. Vibration frequencies of the mixed formulation element are compared with the frequencies obtained from closed-form solutions and finite element analyses. Fundamental frequency is computed with only one element per member span and higher order frequencies are determined with two or four elements with considerable accuracy by employing 3d mixed element and force-based consistent mass matrix.

Study on Flexible Spin-Up Maneuver with Variable Cross-Section Based on Positional FEM

Based on positional finite element method (FEM) and MATLAB platform, program VBEP (Variable cross-section Beam Element based on Positional FEM) is compiled. Flexible spin-up maneuver is calculated. The calculation results show that positional FEM uses fewer elements and gains higher calculation precision and efficiency when compared with traditional nonlinear FEM, and that calculated quantity using lumped mass matrix is less than using consistent mass matrix about properties of materials under the same calculation precision.

Lumped Mass Matrix of Three-Node Beam Element

According to Hamilton theory and the concept of Kinetic energy, lumped mass matrix of three-node beam element based on positional finite element method (FEM) is deduced. By concentrating the mass at the three nodes of beam element, the lumped mass matrix is characterized. When dynamic analysing, lumped mass matrix is simpler and more common than consistent mass matrix because lumped mass matrix is diagonal matrix, and calculation work is less under the same calculation precision.

Finite Element Analysis of Vibrating Frequency for Skew Slab Bridge Based on Finite Strip Thought

Based on the finite strip thought and displacement interpolation function of Bernoulli-Euler beam element, using the transformation relationship between skew coordinate and Cartesian coordinate system, a new kind of thin parallel slab element was established, element stiffness matrix and consistent mass matrix were derived. The vibrating frequency of simply supported skewed slab was calculated. Computing results were compared with theoretical results and Ansys results. The maximum error was 2.68%. Changing the mesh density of skew slab, the convergence of present element was tested. Examples show that this element has the features of high precision and strong convergence. At last, the vibrating frequency coefficients of skew slab bridge with different ratios of span to width were provided, which can be adopted to compute the vehicle’s impact factor of skew slab bridge by specification method.