# Nonlinear Problems

• Friedel Hartmann
• Peter Jahn
Chapter
Part of the Springer Series in Solid and Structural Mechanics book series (SSSSM, volume 13)

## Abstract

In this chapter we discuss nonlinear problems. The focus is on the questions, which parts of the algebra of finite elements can be directly transferred to the nonlinear theory and where the nonlinear theory differs from the linear theory and what are the characteristic features of nonlinear theories.

## References

1. 1.
Dhatt G, Touzot G, Lefrançois (2012) Finite element method. Wiley, ISTEGoogle Scholar
2. 2.
Hartmann F (1985) The mathematical foundation of structural mechanics. Springer, HeidelbergGoogle Scholar
3. 3.
Wriggers P (2010) Nonlinear finite element methods. Springer, HeidelbergGoogle Scholar
4. 4.
Gruttmann F, Sauer R, Wagner W (2000) Theory and numerics of three-dimensional beams with elastoplastic behaviour. Int J Num Methods Eng 48(12):1675–1702
5. 5.
Strang G (2019) Linear algebra and learning from data. Wellesley-Cambridge PressGoogle Scholar
6. 6.
Hartmann F (2013) Green’s functions and finite elements. Springer, HeidelbergGoogle Scholar
7. 7.
Bangerth W, Rannacher R (2003) Adaptive finite element methods for differential equations. Birkhäuser Basel Boston BerlinGoogle Scholar

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

## Authors and Affiliations

• Friedel Hartmann
• 1
• Peter Jahn
• 1
1. 1.Institute of Structural MechanicsUniversity of KasselKasselGermany
{"ft_lang_label":"__label__en","ft_lang_prob":0.68768156,"math_prob":0.4294942,"size":1372,"snap":"2021-04-2021-17","text_gpt3_token_len":323,"char_repetition_ratio":0.14400585,"word_repetition_ratio":0.0,"special_character_ratio":0.22886297,"punctuation_ratio":0.12888889,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.96225464,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2021-01-19T06:08:14Z\",\"WARC-Record-ID\":\"<urn:uuid:e502a875-1210-4787-bb55-eb1be08caa87>\",\"Content-Length\":\"64137\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:0f5e7477-760d-4dc3-9402-d5c6c0330e19>\",\"WARC-Concurrent-To\":\"<urn:uuid:c55406f4-a0e1-4f18-8af3-45c4d12f8b32>\",\"WARC-IP-Address\":\"151.101.200.95\",\"WARC-Target-URI\":\"https://link.springer.com/chapter/10.1007%2F978-3-030-55889-5_8\",\"WARC-Payload-Digest\":\"sha1:QBNF3WOOW367GIMDNLVR7MNIQVZJFGB5\",\"WARC-Block-Digest\":\"sha1:Q6HAIYLIJHQPCS65L3WBB3A7ARQTJEHL\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2021/CC-MAIN-2021-04/CC-MAIN-2021-04_segments_1610703517966.39_warc_CC-MAIN-20210119042046-20210119072046-00201.warc.gz\"}"}