New strong formulation for material nonlinear problems based on the particle difference method

2019 ◽  
Vol 98 ◽  
pp. 310-327 ◽  
Author(s):  
Young-Cheol Yoon ◽  
Peter Schaefferkoetter ◽  
Timon Rabczuk ◽  
Jeong-Hoon Song
Keyword(s):  
Difference Method ◽  
Nonlinear Problems ◽  
Material Nonlinear ◽  
Strong Formulation

A FAST COMPUTATION METHOD FOR SOFT TISSUE DEFORMATIONS SIMULATION BASED ON SELF-SELECTION ALGORITHM FOR EMBEDDED OPERATING AREA

2017 ◽  
Vol 17 (07) ◽  
pp. 1740016
Author(s):  
MONAN WANG ◽  
ZHIYONG MAO ◽  
XIANJUN AN
Keyword(s):  
Soft Tissue ◽  
Soft Tissues ◽  
Nonlinear Problems ◽  
Rectus Femoris ◽  
Computation Method ◽  
Biomechanical Models ◽  
Simulation Based ◽  
Material Nonlinear ◽  
Tissue Deformations ◽  
Tissue Models

This study used biomechanical models of soft tissues based on combined exponential and polynomial models. Finite element methods were used to solve material nonlinear and geometrically nonlinear problems of soft tissue models. This involved assigning a screening coefficient in the model-accelerated computing process to filter the units involved in the calculation. The screening coefficient controlled both the accuracy of the results of simulation and the computing speed through setting up a subset of finite elements. The fast computer method based on the screening coefficient was applied to the rectus femoris simulation.

Straight Beams Rested on Nonlinear Elastic Foundations – Part 1 (Theory, Experiments, Numerical Approach)

2014 ◽  
Vol 684 ◽  
pp. 11-20 ◽  
Author(s):  
Karel Frydrýšek ◽  
Šárka Michenková ◽  
Marek Nikodým
Keyword(s):  
Difference Method ◽  
Least Squares Method ◽  
Reaction Force ◽  
Nonlinear Problems ◽  
Numerical Approach ◽  
Nonlinear Dependence ◽  
Central Difference ◽  
Central Difference Method ◽  
Nonlinear Elastic ◽  
Numerical Approaches

This paper presents theory, experiments and numerical approaches suitable for the solution of straight plane beams rested on an elastic (Winkler's) foundation, including nonlinearities. The nonlinear dependence of the reaction force on displacement in the foundation (i.e. the experimental data) can be described via bilateral linear or bilateral linear + cubic or bilateral linear + cubic + quintic approximations, or by unilateral approximation (i.e. by using the Least Squares Method). These applications lead to linear or nonlinear differential 4th-order equations. For solutions of nonlinear problems of mechanics, the Finite Difference Method (i.e. the Central Difference Method) and boundary conditions are applied. The solution and its evaluation is performed in second part of this article.

Straight Beams Rested on Nonlinear Elastic Foundations – Part 2 (Numerical Solutions, Results and Evaluation)

2014 ◽  
Vol 684 ◽  
pp. 21-29 ◽  
Author(s):  
Šárka Michenková ◽  
Karel Frydrýšek ◽  
Marek Nikodým
Keyword(s):  
Difference Method ◽  
Numerical Solutions ◽  
Nonlinear Problems ◽  
Central Difference ◽  
Practical Applications ◽  
Reaction Forces ◽  
Central Difference Method ◽  
Linear And Nonlinear ◽  
Nonlinear Elastic ◽  
Nonlinear Solutions

This paper presents numerical solutions of straight plane beam structures rested on an elastic (Winkler's) foundation. It is a continuation of our previous work (see Part 1 of this article) focused on practical applications and solutions including nonlinearities in the foundation (i.e. bilateral linear, bilateral linear + cubic, bilateral linear + cubic + quintic approximations and unilateral approximation for dependencies of reaction forces on deflection in the foundation). For solutions of nonlinear problems of mechanics (i.e. differential 4th-order equations), the Finite Difference Method (i.e. the Central Difference Method) is applied in combination with the Newton (Newton–Raphson) Method. Finally, in one example, linear and nonlinear approaches are solved, evaluated and compared. In some cases, there are evident major differences between the linear and nonlinear solutions.

scholarly journals Mathematical modeling of materially nonlinear problems in structural analyses, Part II: Application in contemporary software

2010 ◽  
Vol 8 (2) ◽  
pp. 201-210 ◽  
Author(s):  
Zoran Bonic ◽  
Todor Vacev ◽  
Verka Prolovic ◽  
Marina Mijalkovic ◽  
Petar Dancevic
Keyword(s):  
Mathematical Modeling ◽  
Nonlinear Problems ◽  
Load Level ◽  
Nonlinear Material ◽  
Material Models ◽  
Spread Footing ◽  
Material Nonlinear ◽  
Theoretical Foundations ◽  
Increasing Load ◽  
Good Agreement

The paper presents application of nonlinear material models in the software package Ansys. The development of the model theory is presented in the paper of the mathematical modeling of material nonlinear problems in structural analysis (part I - theoretical foundations), and here is described incremental-iterative procedure for solving problems of nonlinear material used by this package and an example of modeling of spread footing by using Bilinear-kinematics and Drucker-Prager mode was given. A comparative analysis of the results obtained by these modeling and experimental research of the author was made. Occurrence of the load level that corresponds to plastic deformation was noted, development of deformations with increasing load, as well as the distribution of dilatation in the footing was observed. Comparison of calculated and measured values of reinforcement dilatation shows their very good agreement.

Natural Element Method for Material and Geometrical Bi-Nonlinear Problems

2012 ◽  
Vol 166-169 ◽  
pp. 93-97
Author(s):  
Dao Hong Ding ◽  
Qing Zhang ◽  
Jiang Qing Xiao
Keyword(s):  
Interpolation Method ◽  
Constitutive Relations ◽  
Nonlinear Problems ◽  
Shape Functions ◽  
Natural Neighbor ◽  
Kronecker Delta ◽  
Natural Element Method ◽  
Natural Element ◽  
Material Nonlinear ◽  
Element Method

Based on the Voronoi diagram of some nodes, the natural element method (NEM) constructs the shape functions by the natural neighbor interpolation method, and its shape functions satisfy the Kronecker delta property, which makes it impose essential boundary conditions easily. Based on the geometrical nonlinear relations and material nonlinear constitutive relations, we extend the NEM to material and geometrical bi-nonlinear problems in this paper. Numerical examples show that the NEM is effective, rational and feasible in dealing with problems of both material and geometrical bi-nonlinear.

Sign in / Sign up

Export Citation Format

Share Document