Finite Element Method - The Basis (Volume 1)

xiiContents16.6 Galerkin weighting and ®nite volume methods 45116.7 Use of hierarchic and special functions based on standard ®niteelements satisfying the partition of unity requirement 45716.8 Closure 464References 46417. The time dimension ± semi-discretization of ®eld and dynamic problemsand analytical solution procedures 46817.1 Introduction 46817.2 Direct formulation of time-dependent problems with spatial ®niteelement subdivision 46817.3 General classi®cation 47617.4 Free response ± eigenvalues for second-order problems anddynamic vibration 47717.5 Free response ± eigenvalues for ®rst-order problems and heatconduction, etc. 48417.6 Free response ± damped dynamic eigenvalues 48417.7 Forced periodic response 48517.8 Transient response by analytical procedures 48617.9 Symmetry and repeatability 490References 49118. The time dimension ± discrete approximation in time 49318.1 Introduction 49318.2 Simple time-step algorithms for the ®rst-order equation 49518.3 General single-step algorithms for ®rst- and second-order equations 50818.4 Multistep recurrence algorithms 52218.5 Some remarks on general performance of numerical algorithms 53018.6 Time discontinuous Galerkin approximation 53618.7 Concluding remarks 538References 53819. Coupled systems 54219.1 Coupled problems ± de®nition and classi®cation 54219.2 Fluid±structure interaction (Class I problem) 54519.3 Soil±pore ¯uid interaction (Class II problems) 55819.4 Partitioned single-phase systems ± implicit±explicit partitions(Class I problems) 56519.5 Staggered solution processes 567References 57220. Computer procedures for ®nite element analysis 57620.1 Introduction 57620.2 Data input module 57820.3 Memory management for array storage 58820.4 Solution module ± the command programming language 59020.5 Computation of ®nite element solution modules 597