On the representation of three-dimensional elasticity solutions with the aid of complex valued functions
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Publication:1263320
DOI10.1007/BF00055333zbMath0687.73008MaRDI QIDQ1263320
Publication date: 1989
Published in: Journal of Elasticity (Search for Journal in Brave)
completenessregular solutionscomplex Muskhelishvili formulation for plane strainNeuber/Papkovich solutionsix complex valued functionsthree-dimensional displacement fields
Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Integral representations, integral operators, integral equations methods in higher dimensions (31B10)
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Overview about Solution Representations for Elasticity Problems and Some Selected Particular Solutions ⋮ The application of a complex 3-dimensional elasticity solution representation for the analysis of a thick rectangular plate ⋮ Application of a direct Trefftz method with domain decomposition to 2D potential problems ⋮ Generalized finite differences using fundamental solutions ⋮ Some remarks on Trefftz type approximations ⋮ The derivation of a thick and thin plate formulation without ad hoc assumptions ⋮ Formulation of hybrid Trefftz finite element method for elastoplasticity ⋮ ψ-Hyperholomorphic functions and a Kolosov-Muskhelishvili formula
Cites Work
- On regular and singular harmonic functions of three variables
- On singularities of solutions of partial differential equations in three variables
- The use of complex valued functions for the solution of three-dimensional elasticity problems
- On the existence, uniqueness and completeness of displacements and stress functions in linear elasticity
- On the representation of elastic displacement fields in terms of three harmonic functions
- Whittaker's Work on the Integral Representation of Harmonic Functions
- On the completeness of the Papkovich potentials
- Completeness of the Papkovich potentials
- A Class of Harmonic Functions in Three Variables and Their Properties
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