本书研究的特征问题包括结构工程领域的重要问题，如梁和壳结构的自由振动、弹性稳定性、屈曲和损伤诱发扰动，以及数学上具有挑战性的向量型Sturm-Liouville特征值问题。本征问题属于一类典型的非线性问题，如何高效地获得高精度的连续阶特征值与特征函数具有很大的挑战性，解答的精度和效率对数值方法提出了很高的要求。本书发展了高性能的h和hp型自适应有限元算法和方法，以获得梁和壳体的振动、稳定和损伤扰动的高精度解决方案。该书主要包括以下内容：（1）向量型Sturm-Liouville特征问题的自适应有限元法，（2）非均匀变曲率梁振动的自适应有限元法，（3）含裂纹损伤梁振动扰动的自适应有限元法，（4）裂纹梁损伤识别的自适应有限元法，（5）含裂纹损伤梁稳定扰动的自适应有限元法，（6）圆柱壳振动的自适应有限元法，（7）圆柱壳振动的改进hp型自适应有限元法，（8）含裂纹损伤圆柱壳振动扰动的自适应有限元法。
本书可以作为土木工程、工程力学和计算数学专业的研究人员、研究生和本科生的参考书。

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