A High-Order Numerical Manifold Method Based on B-Spline Interpolation and its Application in Structural Dynamics

2016 ◽  
Vol 08 (08) ◽  
pp. 1650093 ◽  
Author(s):  
Wei-Bin Wen ◽  
Kai Yao ◽  
Hong-Shuai Lei ◽  
Sheng-Yu Duan ◽  
Dai-Ning Fang
Keyword(s):  
Polynomial Interpolation ◽  
Dynamic Equilibrium ◽  
Spline Interpolation ◽  
Numerical Manifold Method ◽  
Equilibrium Equations ◽  
Energy Principle ◽  
Static And Dynamic Analysis ◽  
Computation Efficiency ◽  
Quintic Polynomial ◽  
Numerical Manifold

In this paper, a new numerical manifold method (NMM) is formulated on the basis of quintic polynomial interpolation. For linear elastodynamics analysis, the generalized instantaneous potential energy principle for the NMM is employed to obtain the formulation of its elastodynamic equilibrium equations. For the presented NMM, the penalty method is designed to deal with the boundary conditions. The initialization of the dynamic equilibrium equation coupled with its time integration method is exclusively designed. The proposed NMM is applied for static and dynamic analysis of an elastic beam to verify the validity of the proposed NMM. The calculation accuracy and computation efficiency analysis are conducted by comparing the NMM with the finite element method (FEM). Numerical result comparison shows that the proposed NMM possesses higher calculation accuracy than the FEM, especially for the gradient solutions. Time consumption analysis demonstrates that the proposed NMM provides far more accurate numerical results with lower time cost than the FEM.

Static and dynamic analysis of timber shear walls

1990 ◽  
Vol 17 (4) ◽  
pp. 643-651 ◽  
Author(s):  
A. Filiatrault
Keyword(s):  
Dynamic Equilibrium ◽  
Load Capacity ◽  
Shear Walls ◽  
Lateral Stiffness ◽  
Analysis Model ◽  
Equilibrium Equations ◽  
Seismic Behaviour ◽  
Nonlinear Load ◽  
Static And Dynamic Analysis ◽  
Timber Shear Walls

Light-frame wood structures have evolved in recent years to the point where their earthquake resistance is now questionable. Shear walls are commonly used to provide lateral stiffness and strength in wood buildings. Therefore, accurate predictions of the seismic behaviour of timber shear walls are necessary in order to evaluate the safety of existing timber buildings and improve design practice. This paper develops and validates a simple structural analysis model to predict the behaviour of timber shear walls under lateral static loads and earthquake excitations. The model is restricted to two-dimensional shear walls with arbitrary geometry. The nonlinear load –slip characteristics of the fasteners are used in a displacement-based energy formulation to yield the static and dynamic equilibrium equations. The model is embedded in a shear wall analysis program (SWAP) developed for microcomputer applications. The predictions of the model are compared with full-scale racking and shake table tests. The ability of the model to accurately predict the lateral stiffness, the ultimate lateral load capacity, and the complete earthquake response of timber shear walls is clearly demonstrated. Key words: dynamics, earthquakes, seismic response, timber construction, walls, wood.

Three-Dimensional Numerical Manifold Method Based on Hexahedron Element with Full First-Order Cover Function and its Application in Underground Excavation

2007 ◽  
Vol 340-341 ◽  
pp. 365-370 ◽  
Author(s):  
Y.H. Zhang ◽  
Qian Sheng ◽  
Y.M. Cheng
Keyword(s):  
Three Dimensional ◽  
Shear Stiffness ◽  
Surface Force ◽  
Inertia Force ◽  
Numerical Manifold Method ◽  
Underground Excavation ◽  
Equilibrium Equations ◽  
First Order ◽  
Numerical Manifold ◽  
Cover Function

In this paper, three-dimensional(3D) Numerical Manifold Method (NNM) based on hexahedron element cover with full first-order cover function is proposed and the shape function of C8 isoparametric element in FEM is used as the cover weight function. All sub-matrices in equilibrium equations, including stiffness matrix, initial stress matrix, point force matrix, surface force matrix, body force matrix, inertia force matrix, contact matrix and friction matrix, are derived. Different with 2D contact, the direction of shear stiffness and friction force can not be easily defined in 3D contact. A new iterative method based on vector theory to detect the contact direction is developed. The application of 3D NMM in underground excavation is also presented and show good agreement with real engineering.

scholarly journals Time-dependent deformation and failure of granite based on the virtual crack incorporated numerical manifold method

2021 ◽  
Vol 133 ◽  
pp. 104070
Author(s):  
Xian-yang Yu ◽  
Tao Xu ◽  
Michael J. Heap ◽  
Patrick Baud ◽  
Thierry Reuschlé ◽  
...  
Keyword(s):  
Time Dependent ◽  
Numerical Manifold Method ◽  
Deformation And Failure ◽  
Numerical Manifold

scholarly journals Dynamic Equilibrium Equations in Unified Mechanics Theory

2021 ◽  
Vol 2 (1) ◽  
pp. 63-80
Author(s):  
Noushad Bin Jamal Bin Jamal M ◽  
Hsiao Wei Lee ◽  
Chebolu Lakshmana Rao ◽  
Cemal Basaran
Keyword(s):  
Energy Loss ◽  
Entropy Generation ◽  
Equilibrium Equation ◽  
Dynamic Equilibrium ◽  
Free Vibration Analysis ◽  
Newtonian Mechanics ◽  
Equilibrium Equations ◽  
Time Coordinate ◽  
Proposed Model ◽  
Laws Of Thermodynamics

Traditionally dynamic analysis is done using Newton’s universal laws of the equation of motion. According to the laws of Newtonian mechanics, the x, y, z, space-time coordinate system does not include a term for energy loss, an empirical damping term “C” is used in the dynamic equilibrium equation. Energy loss in any system is governed by the laws of thermodynamics. Unified Mechanics Theory (UMT) unifies the universal laws of motion of Newton and the laws of thermodynamics at ab-initio level. As a result, the energy loss [entropy generation] is automatically included in the laws of the Unified Mechanics Theory (UMT). Using unified mechanics theory, the dynamic equilibrium equation is derived and presented. One-dimensional free vibration analysis with frictional dissipation is used to compare the results of the proposed model with that of a Newtonian mechanics equation. For the proposed entropy generation equation in the system, the trend of predictions is comparable with the reported experimental results and Newtonian mechanics-based predictions.

Sign in / Sign up

Export Citation Format

Share Document