本書研究的特征問題包括結(jié)構(gòu)工程領(lǐng)域的重要問題，如梁和殼結(jié)構(gòu)的自由振動(dòng)、彈性穩(wěn)定性、屈曲和損傷誘發(fā)擾動(dòng)，以及數(shù)學(xué)上具有挑戰(zhàn)性的向量型Sturm-Liouville特征值問題。本征問題屬于一類典型的非線性問題，如何高效地獲得高精度的連續(xù)階特征值與特征函數(shù)具有很大的挑戰(zhàn)性，解答的精度和效率對數(shù)值方法提出了很高的要求。本書發(fā)展了高性能的h和hp型自適應(yīng)有限元算法和方法，以獲得梁和殼體的振動(dòng)、穩(wěn)定和損傷擾動(dòng)的高精度解決方案。
本書可以作為土木工程、工程力學(xué)和計(jì)算數(shù)學(xué)專業(yè)的研究人員、研究生和本科生的參考書。
Chapter 1 Introduction
1.1 Introduction
1.2 Basic procedures and categories of high-performance adaptive finite element method
1.3 Applications of adaptive finite element method in eigenproblems of beam and shell: Vibration, stability, and damage disturbance
1.4 Research aims and contents of the book
References
Chapter 2 Adaptive finite element method for vector Sturm-Liouville eigenproblems
2.1 Introduction
2.2 Adaptive approach for eigenproblems in systems of ordinary differential equations
2.2.1 Eigenproblems in system of second order ordinary differential equations
2.2.2 Stop criterion and adaptive procedure
2.3 Finite element solutions of eigenpairs
2.3.1 Finite element discretisation
2.3.2 Inverse iteration for single eigenpairs
2.3.3 Subspace iteration for coincident eigenpairs
2.4 Error estimation for eigenfunctions
2.5 h-version mesh refinement
2.6 Numerical examples
2.6.1 Example 1: Coefficients of variable matrices and adjacent approximate eigenvalues
2.6.2 Example 2: Benchmark eigenproblems in SL12F
2.6.3 Example 3: Coefficients of constant matrices and coincident eigenvalues
2.6.4 Example 4: Free vibration of planar elliptic beams
2.7 Conclusions
References
Chapter 3 Adaptive finite element method for vibration of non-uniform and variable curvature beams
3.1 Introduction
3.2 Partial differential governing equations for in-plane and out-of-plane free vibration of variable geometrical Timoshenko beams
3.3 Finite element discretisation
3.4 Superconvergent patch recovery of vibration modes
3.5 Error estimation and mesh refinement
3.6 Finite element mesh refinement strategy and procedure
3.7 Numerical examples
3.7.1 Example 1: In-plane vibration of a parabolic curved beam
3.7.2 Example 2: In-plane vibration of a beam with variable cross-section and curvature
3.7.3 Example 3: In-plane vibration of an elliptically curved beam
3.7.4 Example 4: Out-of-plane vibration of a parabolic curved beam
3.7.5 Example 5: Out-of-plane vibration of a circularly curved beam
3.8 Conclusions
References
Chapter 4 Adaptive finite element method for vibration disturbance of cracked beams
4.1 Introduction
4.2 Characterisation method for microcrack damage in circularly curved beams
4.3 Partial differential governing equations and finite element discretisation for free vibration of circularly curved beams
4.4 Local mesh refinement techniques and procedure
4.5 Numerical examples
4.5.1 Example 1: Verification for eigensolutions of free vibration of uncracked curved beam
4.5.2 Example 2: Different depths of single-crack beams
4.5.3 Example 3: Different numbers of multiple-crack damage
4.5.4 Example 4: Different distributions of multiple-crack damage
4.6 Conclusions
References
Chapter 5 Adaptive finite element method for damage detection of cracked beams
5.1 Introduction
5.2 Adaptive approach for damage detection of cracked beams
5.2.1 Formulation and analogy of cracked beams
5.2.2 Stop criterion
5.2.3 Analysis strategy
5.3 Adaptive analysis
5.3.1 Finite element solution
5.3.2 Error estimation and mesh refinement
5.4 Newton-Raphson iteration
5.5 Damage refinement
5.6 Algorithms
5.7 Numerical examples
5.7.1 Example 1: Double-clamped uncracked beam with a sinusoidal cross section
5.7.2 Example 2: Stepped cantilever beam with a single crack
5.7.3 Example 3: Cantilever beam with double cracks
5.7.4 Example 4: Cantilever beam with triple cracks
5.7.5 Example 5: Double-clamped uncracked beam with a sinusoidal cross section
5.7.6 Example 6: Stepped cantilever beam with a single crack
5.7.7 Example 7: Cantilever beam with double cracks
5.7.8 Example 8: Cantilever beam with triple cracks
5.8 Conclusions
References
Chapter 6 Adaptive finite element method for stability disturbance of cracked beams
6.1 Introduction
6.2 Elastic buckling of circularly curved beams based on Euler-Bernoulli theory
6.3 Characterisation method for micro-crack damage in circularly curved beams
6.4 Local mesh refinement techniques and procedure
6.5 Numerical examples
6.5.1 Example 1: Verification for eigensolutions and refined meshes of elastic buckling of uncracked curved beam
6.5.2 Example 2: Buckling loads under different subtended angles
6.5.3 Example 3: Different locations of single crack damage
6.5.4 Example 4: Different depths of single crack damage
6.5.5 Example 5: Different distributions of multiple crack damage
6.6 Conclusions
References
Chapter 7 Adaptive finite element method for vibration of cylindrical shells
7.1 Introduction
7.2 Partial differential governing equations for the free vibration of rotating cylindrical shells
7.3 Mesh refinement procedure of finite element method
7.4 Finite element discretisation
7.5 Error estimation
7.6 Element subdivision and mesh refinement
7.7 Numerical examples
7.7.1 Example 1: Thin-wall thickness
7.7.2 Example 2: Moderately thick-wall thickness
7.7.3 Example 3: Different circumferential wave numbers and thickness-to-length ratios
7.7.4 Example 4: Hinged-hinged and clamped- clamped boundary conditions
7.8 Conclusions
References
Chapter 8 Improved hp-version adaptive finite element method for vibration of cylindrical shells
8.1 Introduction
8.2 Differential equations describing the free vibration of moderately thick circular cylindrical shells
8.3 Finite element discretisation and solutions of the differential equations
8.3.1 Higher-order Lagrange shape functions
8.3.2 Finite element discretisation
8.3.3 Inverse iteration technique for eigensolutions
8.4 hp-version adaptive finite element method via error homogenisation and higher-order interpolation
8.4.1 h-version mesh refinement
8.4.2 p-version higher-order interpolation
8.5 Global algorithm and procedure
8.6 Numerical examples
8.6.1 Example 1: h-version and hp-version adaptive finite element analysis
8.6.2 Example 2: Thin-walled circular cylindrical shells
8.6.3 Example 3: Circumferential wave number n
8.6.4 Example 4: Ratio of thickness to radius h/r
8.6.5 Example 5: Ratio of thickness to length h/l
8.7 Conclusions
References
Chapter 9 Adaptive finite element method for vibration disturbance of cracked cylindrical shells
9.1 Introduction
9.2 Differential equations describing the free vibration of moderately thick circular cylindrical shell
9.3 Damage characterisation method for circumferential cracks in circular cylindrical shell
9.4 h-version mesh refinement method for eigensolutions of cracked circular cylindrical shell
9.4.1 Finite element solutions
9.4.2 Error estimation
9.4.3 Element subdivision and refinement
9.5 Global algorithm and procedure
9.6 Numerical examples
9.6.1 Example 1: Benchmarks for free vibration of circular cylindrical shell
9.6.2 Example 2: Verification of frequency solutions of cracked circular cylindrical shell under variable circumferential wave numbers
9.6.3 Example 3: Free vibration disturbance by crack location
9.6.4 Example 4: Free vibration disturbance by crack depth
9.6.5 Example 5: Free vibration disturbance by number of multiple cracks
9.7 Conclusions
References
Chapter 10 Summary and prospect
10.1 Summary
10.2 Prospect
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