Harmonic differential quadrature method and applications to analysis of structural components

1995 ◽  
Vol 111 (1-2) ◽  
pp. 85-94 ◽  
Author(s):  
A. G. Striz ◽  
X. Wang ◽  
C. W. Bert
Keyword(s):  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Structural Components ◽  
Harmonic Differential Quadrature Method

An approach in deformation and stress analysis of elasto-plastic sandwich cylindrical shell panels based on harmonic differential quadrature method

2016 ◽  
Vol 19 (2) ◽  
pp. 167-191 ◽  
Author(s):  
H Shokrollahi ◽  
F Fallah ◽  
MH Kargarnovin
Keyword(s):  
Cylindrical Shell ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Core Material ◽  
Quadrature Method ◽  
Sandwich Shell ◽  
Finite Element Software ◽  
The Core ◽  
Harmonic Differential Quadrature Method ◽  
Shell Panel

Using harmonic differential quadrature method, an approach to analyze sandwich cylindrical shell panels with any sort of boundary conditions under a generally distributed static loading, undergoing elasto-plastic deformation is proposed. The faces of the sandwich shell panel are made of some isotropic materials with linear work hardening behavior while the core is assumed to be an isotropic material experiencing only elastic behavior. The faces are modeled as thin cylindrical shells obeying the Kirchhoff–Love assumptions. For the core material, it is assumed to be thick and the in-plane stresses are negligible. Upon application of an inner and outer general lateral loading, the governing equations are derived using the principle of virtual displacements. Using an iterative approach, named elasto-plastic harmonic differential quadrature method (EP-HDQM), the equations are solved. The obtained results are compared with the results from finite element software Ansys for different sandwich shell panel configurations. Then, the effects of changing different parameters on the stress and displacement components of sandwich cylindrical shell panels in different elasto-plastic conditions are investigated.

Harmonic Differential Quadrature Method for Surface Location Error Prediction and Machining Parameter Optimization in Milling

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Ye Ding ◽  
XiaoJian Zhang ◽  
Han Ding
Keyword(s):  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Machining Parameters ◽  
Quadrature Method ◽  
Location Error ◽  
Sampling Grid ◽  
Surface Location Error ◽  
Harmonic Differential Quadrature Method ◽  
Surface Location ◽  
Grid Points

This paper presents a semi-analytical numerical method for surface location error (SLE) prediction in milling processes, governed by a time-periodic delay-differential equation (DDE) in state-space form. The time period is discretized as a set of sampling grid points. By using the harmonic differential quadrature method (DQM), the first-order derivative in the DDE is approximated by the linear sums of the state values at all the sampling grid points. On this basis, the DDE is discretized as a set of algebraic equations. A dynamic map can then be constructed to simultaneously determine the stability and the steady-state SLE of the milling process. To obtain optimal machining parameters, an optimization model based on the milling dynamics is formulated and an interior point penalty function method is employed to solve the problem. Experimentally validated examples are utilized to verify the accuracy and efficiency of the proposed approach.

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