The Global Secant Relaxation-Based Accelerated Iteration Procedure for Solution of Nonlinear Finite Element Equation Systems of Offshore Structural Mechanics Problems

2011 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Finite Element ◽  
Nonlinear Problems ◽  
Iterative Solution ◽  
Structural Mechanics ◽  
Iteration Scheme ◽  
Nonlinear Finite Element ◽  
Constant Stiffness ◽  
Iterative Computation ◽  
Newton Raphson ◽  
Quasi Newton

A global secant relaxation (GSR)-based accelerated iteration scheme can be used to carry out the incremental/iterative solution of various nonlinear finite element systems of offshore structural mechanics problems. This computation procedure can overcome the possible deficiency of numerical instability caused by local failure existing in the iterative computation. Moreover, this method can efficiently accelerate the convergency of the iterative computation. This incremental/iterative analysis can consistently be carried out to update the response history up to a near ultimate load stage, which is important for investigating the global failure behaviour of a structure under certain external cause, if the constant stiffness is used. Consequently, this method can widely be used to solve general nonlinear problems. Mathematical procedures of Newton-Raphson techniques in finite element methods for nonlinear finite element problems are summarized. These techniques are the Newton-Raphson method, quasi-Newton methods, modified Newton-Raphson methods and accelerated modified Newton-Raphson methods. Numerical results obtained by using various accelerated modified Newton-Raphson methods are used to study the convergency performances of these techniques for material nonlinearity problems and deformation nonlinearity problems, separately.

An adaptive nonlinear finite element analysis of minimal surface problem based on element energy projection technique

2020 ◽  
Vol 37 (8) ◽  
pp. 2847-2869
Author(s):  
Kaifeng Jiang ◽  
Si Yuan ◽  
Qinyan Xing
Keyword(s):  
Finite Element ◽  
Minimal Surface ◽  
Error Control ◽  
Nonlinear Problems ◽  
Fe Analysis ◽  
Nonlinear Finite Element ◽  
Maximum Norm ◽  
Element Analysis ◽  
Content Type ◽  
Element Energy Projection

Purpose This paper aims to propose a new adaptive strategy for two-dimensional (2D) nonlinear finite element (FE) analysis of the minimal surface problem (MSP) based on the element energy projection (EEP) technique. Design/methodology/approach By linearizing nonlinear problems into a series of linear problems via the Newton method, the EEP technique, which is an effective and reliable point-wise super-convergent displacement recovery strategy for linear FE analysis, can be directly incorporated into the solution procedure. Accordingly, a posteriori error estimate in maximum norm was established and an adaptive 2D nonlinear FE strategy of h-version mesh refinement was developed. Findings Three classical known surfaces, including a singularity problem, were analysed. Moreover, an example whose analytic solution is unavailable was considered and a comparison was made between present results and those computed by the MATLAB PDE toolbox. The results show that the adaptively-generated meshes reflect the difficulties inherent in the problems and the proposed adaptive analysis can produce FE solutions satisfying the user-preset error tolerance in maximum norm with a fair adaptive convergence rate. Originality/value The EEP technique for linear FE analysis was extended to the nonlinear procedure of MSP and can be expected to apply to other 2D nonlinear problems. The employment of the maximum norm makes point-wisely error control on the sought surfaces possible and makes the proposed method distinguished from other adaptive FE analyses.

Dynamic Wrinkling of Viscoelastic Membranes

1993 ◽  
Vol 60 (3) ◽  
pp. 575-582 ◽  
Author(s):  
C. H. Jenkins ◽  
J. W. Leonard
Keyword(s):  
Finite Element ◽  
Constitutive Equation ◽  
Strain Energy ◽  
Temporal Integration ◽  
Nonlinear Finite Element ◽  
Analysis Method ◽  
Finite Difference Equation ◽  
Membrane Structures ◽  
Newton Raphson ◽  
Raphson Method

Problems associated with viscoelastic membrane structures have been documented, e.g., dynamic wrinkling and its effects on fatigue analysis and on snap loading. In the proposed analysis method, the constitutive equation is approximated by a finite difference equation and embedded within a nonlinear finite element spatial discretization. Implicit temporal integration and a modified Newton-Raphson method are used within a time increment. The stress-strain hereditary relation is formally derived from thermodynamic considerations. Use of modified strain-energy and dissipation functions facilitates the description of wrinkling during the analysis. Applications are demonstrated on an inflated cylindrical cantilever and on a submerged cylindrical membrane excited by waves.

Structural mechanics characterization of steel intermeshed connection using nonlinear finite element analysis

2021 ◽  
Vol 238 ◽  
pp. 112264
Author(s):  
Mohammad E. Shemshadian ◽  
Arturo E. Schultz ◽  
Jia-Liang Le ◽  
Debra F. Laefer ◽  
Salam Al-Sabah ◽  
...  
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Nonlinear Finite Element Analysis ◽  
Structural Mechanics ◽  
Nonlinear Finite Element ◽  
Element Analysis

Geometry-Based Stiffness Parameters for Predicting Approach of Limit Points in Finite-Element Studies

1986 ◽  
Vol 108 (4) ◽  
pp. 462-468
Author(s):  
Jami J. Shah ◽  
Henry R. Busby ◽  
Gary L. Kinzel
Keyword(s):  
Finite Element ◽  
External Pressure ◽  
Nonlinear Finite Element ◽  
Structural Stiffness ◽  
Numerical Instability ◽  
Displacement Control ◽  
Buckling Modes ◽  
Newton Raphson ◽  
Limit Points

Several parameters for evaluating the decrease in structural stiffness in nonlinear finite element problems are defined here. Two types of parameters were considered: those that measure the overall softening and those that measure only a selected type of response, such as ovalization or bending. These parameters were used for detecting the approach of limit points in cylinder buckling problems under combined bending and external pressure. This is necessary for determining when the Newton-Raphson scheme should be replaced by displacement control to prevent numerical instability. The two types of parameters used in conjunction provide not only a reliable means for sensing the approach of limit points but also a determination of buckling modes.

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