Rudimentary considerations for effective quasi-newton updates in nonlinear finite element analysis

Lee, Sang H.

doi:10.1016/0045-7949(89)90019-9

Computers & Structures

1989

DOI: 10.1016/0045-7949(89)90019-9

|View full text |Cite

Rudimentary considerations for effective quasi-newton updates in nonlinear finite element analysis

Sang H. Lee¹

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1989

1993

Publication Types

Select...

Article5

Relationship

Self Cite1

Independent4

Authors

Journals

Cited by 7 publications

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Applications of a self‐adaptive algorithm to non‐linear finite element analysis

Lee¹,

Hsieh²

1991

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYA self-adaptive algorithm has been developed and implemented for the implicit time integration of nonlinear finite element analysis. In this algorithm, a proper time increment for the next time step is estimated based on the deformation pattern at the preceding step. The iteration process for the equilibrium employs expeditious methods such as quasi-Newton updates and line searches as well as an adaptive stiffness matrix update strategy for efficiency. Convergence difficulties induced from inadequate prediction of step size or the change in non-linearities are tackled by the bisection method. These procedures were also successfully applied to static problems by ignoring the damping and the inertia forces. The objective of this paper is to demonstrate the applicability and the effectiveness of the adaptive algorithm in a wide spectrum of nonlinear problems. Six example problems are illustrated, some of which are rather novel. As demonstrated in this paper, the self-adaptive algorithm implemented in MSC/NASTRAN is proving to be versatile, accurate and efficient.

show abstract

Applications of a self‐adaptive algorithm to non‐linear finite element analysis

Lee¹,

Hsieh²

1991

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

A survey of quasi‐Newton methods with reduced storage

Papadrakakis

Pantazopoulos

1993

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYA family of non-linear solution methods is investigated based on limited-memory quasi-Newton updates. Depending upon the number of updates and the updating formula, a number of solution schemes may be constructed such as the conjugate-and secant-Newton methods, the conventional and modified Newton-Raphson methods and a variety of quasi-Newton updates. Under the proposed implementation, the preconditioned truncated Lanczos method is used for the solution of the linearized problem in each non-linear iteration. The complete factorization of the stiffness matrix is avoided and large-scale problems can be solved efficiently both in terms of computing time and storage. The non-linear iterative scheme is properly modified to account for loading variation inside the increment in order to be able to trace post-critical equilibrium paths.

show abstract

Expedient implicit integration with adaptive time stepping algorithm for nonlinear transient analysis

Lee¹,

Hsieh²

1990

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Rudimentary considerations for effective quasi-newton updates in nonlinear finite element analysis

Cited by 7 publications

References 9 publications

Applications of a self‐adaptive algorithm to non‐linear finite element analysis

Applications of a self‐adaptive algorithm to non‐linear finite element analysis

A survey of quasi‐Newton methods with reduced storage

Expedient implicit integration with adaptive time stepping algorithm for nonlinear transient analysis

Contact Info

Product

Resources

About