TY  - CHAP
A1  - Staat, Manfred
A1  - Ballmann, J.
T1  - Fundamental aspects of numerical methods for the propagation of multi-dimensional nonlinear waves in solids
T2  - Nonlinear hyperbolic equations : theory, computations methods, and applications ; proceedings of the 2nd International Conference on Nonlinear Hyperbolic Problems, Aachen
N2  - The nonlinear scalar constitutive equations of gases lead to a change in sound speed from point to point as would be found in linear inhomogeneous (and time dependent) media. The nonlinear tensor constitutive equations of solids introduce the additional local effect of solution dependent anisotropy. The speed of a wave passing through a point changes with propagation direction and its rays are inclined to the front. It is an open question whether the widely used operator splitting techniques achieve a dimensional splitting with physically reasonable results for these multi-dimensional problems. May be this is the main reason why the theoretical and numerical investigations of multi-dimensional wave propagation in nonlinear solids are so far behind gas dynamics. We hope to promote the subject a little by a discussion of some fundamental aspects of the solution of the equations of nonlinear elastodynamics. We use methods of characteristics because they only integrate mathematically exact equations which have a direct physical interpretation.
KW  - Nichtlineare Welle
KW  - Nichtlineare Gleichung
KW  - Festkörper
KW  - Elastodynamik
KW  - Multi-dimensional wave propagation
KW  - nonlinear solids
KW  - nonlinear tensor constitutive equation
Y1  - 1989
SP  - 574
EP  - 588
ER  - 
TY  - JOUR
A1  - Staat, Manfred
A1  - Baroud, G.
A1  - Topcu, M.
A1  - Sponagel, Stefan
T1  - Soft Materials in Technology and Biology – Characteristics, Properties, and Parameter Identification
JF  - Bioengineering in Cell and Tissue Research / Artmann, Gerhard M. ; Chien, Shu (Eds.)
Y1  - 2008
SN  - 978-3-540-75408-4
SP  - 253
EP  - 315
PB  - Springer
CY  - Berlin
ER  - 
TY  - GEN
A1  - Staat, Manfred
A1  - Barry, Steve
T1  - Continuum Mechanics with an Introduction to the Finite Element Method / Steve Barry; Manfred Staat. With extensions by Manfred Staat.
N2  - Contents: 1 Introduction 2 One Dimensional Continuum Mechanics 3 Tensors 4 Three Dimensional Stress and Strain 5 Conservation Laws 6 Contiunuum Modelling 7 Plain Problems 8 Questions 9 Reference Information
KW  - Technische Mechanik
KW  - Finite-Elemente-Methode
Y1  - 2006
ER  - 
TY  - BOOK
A1  - Staat, Manfred
A1  - Digel, Ilya
A1  - Trzewik, Jürgen
A1  - Sielemann, Stefanie
A1  - Erni, Daniel
A1  - Zylka, Waldemar
T1  - Symposium Proceedings; 4th YRA MedTech Symposium 2024 : February 1 / 2024 / FH Aachen
Y1  - 2024
SN  - 978-3-940402-65-3
U6  - https://doi.org/10.17185/duepublico/81475
PB  - Universität Duisburg-Essen
CY  - Duisburg
ER  - 
TY  - CHAP
A1  - Staat, Manfred
A1  - Duong, Minh Tuan
T1  - Smoothed Finite Element Methods for Nonlinear Solid Mechanics Problems: 2D and 3D Case Studies
T2  - Proceedings of the National Science and Technology Conference on Mechanical - Transportation Engineering (NSCMET 2016), 13th October 2016, Hanoi, Vietnam, Vol.2
N2  - The Smoothed Finite Element Method (SFEM) is presented as an edge-based and a facebased techniques for 2D and 3D boundary value problems, respectively. SFEMs avoid shortcomings of the standard Finite Element Method (FEM) with lower order elements such as overly stiff behavior, poor stress solution, and locking effects. Based on the idea of averaging spatially the standard strain field of the FEM over so-called smoothing domains SFEM calculates the stiffness matrix for the same number of degrees of freedom (DOFs) as those of the FEM. However, the SFEMs significantly improve accuracy and convergence even for distorted meshes and/or nearly incompressible materials.
Numerical results of the SFEMs for a cardiac tissue membrane (thin plate inflation) and an artery (tension of 3D tube) show clearly their advantageous properties in improving accuracy particularly for the distorted meshes and avoiding shear locking effects.
Y1  - 2016
SP  - 440
EP  - 445
ER  - 
TY  - BOOK
A1  - Staat, Manfred
A1  - Erni, Daniel
T1  - Symposium Proceedings; 3rd YRA MedTech Symposium 2019: May 24 / 2019 / FH Aachen
Y1  - 2019
SN  - 978-3-940402-22-6
U6  - https://doi.org/10.17185/duepublico/48750
PB  - Universität Duisburg-Essen
CY  - Duisburg
ER  - 
TY  - JOUR
A1  - Staat, Manfred
A1  - Fiorini, G. L.
A1  - Lensa, W. von
A1  - Burgazzi, L.
T1  - Reliability Methods for Passive Safety Functions
JF  - Proceedings of the SMiRT 14 Post Conference Seminar No 18 on Passive Safety Features in Nuclear Installations
Y1  - 1997
CY  - Pisa
ER  - 
TY  - JOUR
A1  - Staat, Manfred
A1  - Heitzer, M.
T1  - Limit and Shakedown Analysis for Plastic Safety of Complex Structures
JF  - Transactions of the 14th International Conference on Structural Dynamics in Reactor Technology (SMiRT-14) / Livolant, M. [ed]
Y1  - 1997
N1  - Vol. B, Paper B02/2
SP  - 33
EP  - 40
CY  - Lyon
ER  - 
TY  - JOUR
A1  - Staat, Manfred
A1  - Heitzer, M.
T1  - Limit and Shakedown Analysis with Uncertain Data
JF  - Stochastic optimization techniques : numerical methods and technical applications / Marti, K. [ed]
Y1  - 2002
SN  - 3-540-42889-5
SP  - 241
EP  - 254
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Staat, Manfred
A1  - Heitzer, M.
T1  - Probabilistic limit and shakedown problems
JF  - Numerical Methods for Limit and Shakedown Analysis. Deterministic and Probabilistic Approach. NIC Series Vol. 15 / Ed. by Staat, M; Heitzer, M.
Y1  - 2003
SN  - 3-00-010001-6
SP  - 217
EP  - 268
PB  - John von Neumann Institute for Computing (NIC)
CY  - Jülich
ER  -