Design Oriented Analysis of Structures - A Unified Approach
SOLID MECHANICS AND ITS APPLICATIONS
Volume 95
Series Editor: G.M.L. GLADWELL
Department of Civil Engineering
University of Waterloo
Waterloo, Ontario, Canada N2L 3GI
Aims and Scope of the Series
The fundamental questions arising in mechanics are: Why?, How?, and How much?
The aim of this series is to provide lucid accounts written by authoritative researchers
giving vision and insight in answering these questions on the subject of mechanics as it
relates to solids.
The scope of the series covers the entire spectrum of solid mechanics. Thus it includes
the foundation of mechanics; variational formulations; computational mechanics;
statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and
structures; dynamical systems and chaos; the theories of elasticity, plasticity and
viscoelasticity; composite materials; rods, beams, shells and membranes; structural
control and stability; soils, rocks and geomechanics; fracture; tribology; experimental
mechanics; biomechanics and machine design.
The median level of presentation is the first year graduate student. Some texts are monographs
defining the current state of the field; others are accessible to final year under-
graduates; but essentially the emphasis is on readability and clarity.
Design-Oriented
Analysis of Structures
A Unified Approach
by
URI KIRSCH
Technion,
Israel Institute of Technology, Haifa, Israel
Department of Civil Engineering
TECHNION – Israel Institute of Technology
Haifa, Israel
Preface
This book was developed while I was teaching graduate courses on analysis, design and
optimization of structures, in the United States, Europe and Israel. Structural analysis is
a main part of any design problem, and the analysis often must be repeated many times
during the design process. Much work has been done on design-oriented analysis of
structures recently and many studies have been published. The purpose of the book is
to collect together selected topics of this literature and to present them in a unified
approach. It meets the need for a general text covering the basic concepts and methods
as well as recent developments in this area. This should prove useful to students,
researchers, consultants and practicing engineers involved in analysis and design of
structures. Previous books on structural analysis do not cover most of the material
presented in the book.
The book deals with the problem of multiple repeated analyses (reanalysis) of
structures that is common to numerous analysis and design tasks. Reanalysis is needed
in many areas such as structural optimization, analysis of damaged structures, nonlinear
analysis, probabilistic analysis, controlled structures, smart structures and adaptive
structures. It is related to a wide range of applications in such fields as Aerospace
Engineering, Civil Engineering, Mechanical Engineering and Naval Architecture.
In a typical structural design process, the analysis must be repeated numerous times
due to changes in the size of elements, the material properties, the geometry of the
structure (coordinates of joints), the topology (number and orientation of elements and
joints) and support conditions. The high computational cost involved in repeated
analyses is one of the main obstacles in the solution of structural optimization problems,
and only methods that do not involve many time consuming analyses are useful. In
structural damage analysis, it is necessary to analyze the structure for various changes.
It is difficult to determine a priori what damage scenarios should be checked, and
numerous analyses are required to evaluate various hypothetical scenarios. In nonlinear
analysis the set of updated linear equations must be solved repeatedly many times
during the solution process.
Design-oriented analysis is intended for efficient and accurate repeated analyses of
structures. The book introduces effective computational procedures for reanalysis. The
necessary background material on structural analysis needed in the rest of the book is
summarized in the first two chapters. However, the reader is expected to be familiar
with the basic concepts of matrix analysis of structures. Various analysis models are
considered in the book, including linear and nonlinear analysis, eigenproblems and
design sensitivity analysis. The text does not present a survey on reanalysis methods.
Rather, part 1 concentrates on various concepts and methods that form the basis of the
unified approach presented in part 2. To clarify the presentation, many illustrative
examples and numerical results are demonstrated. No specific system of units is used in
the examples, However, in some examples actual dimensions of the structure and
specified magnitude of forces have been used.
In part 1 (Chapters 1–6) t he basic concepts of design-oriented analysis are introduced
and various reanalysis methods are developed. In part 2 (Chapters 7–12) the concepts
and the methods presented in part 1 are integrated into a unified approach for effective
reanalysis of structures. Recent developments and applications in this area are discussed
in this part of the book. Some sections of the book are necessary for continuity, while
others are needed only for those interested in greater depth in a particular topic. Many
sections are independent and can be omitted, or their order can be changed.
The approach presented in the book is suitable for a wide range of applications. It
combines several advantages in terms of generality, ease-of implementation, flexibility,
efficiency and accuracy. The approach is suitable for various types of changes in the
structure and different types of structures. The solution procedure uses the stiffness
analysis formulation and it can be integrated into available finite element programs.
Calculation of derivatives is not required, and the approach is most attractive in cases
where derivatives are not readily available or not easy to calculate. The accuracy of the
results, and the efficiency of the calculations can be controlled by the level of
simplification and the amount of information considered. Highly accurate results can be
achieved at the expense of more computational effort by considering high-order
approximations. On the other hand, very efficient solutions can be obtained by
simplified low-order approximations. In certain cases exact solutions can be achieved
with a small computational effort.
Chapter 1 presents introductory material on analysis and reanalysis of structures.
Various types of changes in the structure are discussed, including changes in the
structural model itself, and the scope of the text is described.
In Chapter 2 some background material on analysis of structures is introduced.
Linear elastic analysis, analysis of continuum structures, nonlinear analysis and
dynamic analysis are briefly described.
Chapter 3 deals with the statement of reanalysis problems. Formulations of linear,
nonlinear and eigenproblem reanalysis are presented and various direct as well as
approximate reanalysis methods are reviewed.
Direct methods, giving exact closed-form solutions, are presented in Chapter 4.
These methods are efficient in situations where a relatively small proportion of the
structure is changed (e.g., changes in cross sections of only a small number elements).
Chapter 5 presents the most simple and most efficient local approximations. These
include the common Taylor series, the binomial series, simplified first-order
approximations and improved series approximations.
In Chapter 6 we describe global approximations such as polynomial-fitting
techniques, the response surface approach, reduced basis methods and the conjugate
gradient method. These approximations are usually obtained by analyzing the structure
at a number of design points, and they are valid for large changes in the structure.
Chapter 7 presents the combined approximations approach. The basic concepts of
combining various methods into a unified solution approach are introduced. The
advantage is that the efficiency of local approximations and the improved accuracy of
global approximations are combined to obtain effective solution procedures. Some
typical cases, where exact or accurate solutions can be achieved, are developed.
Chapter 8 describes simplified solution procedures that can be derived from the
general approach. The various procedures include approximate and most efficient
techniques as well as direct methods that provide exact solutions. We can view some
conventional approximations and direct methods as particular cases of the general
approach presented.
In Chapter 9 we discuss reanalysis for topological and geometrical changes.
Developing reanalysis methods for such changes is most challenging, since the
structural model itself is changed. Both approximate and exact solutions are
demonstrated for various cases of deletion and addition of elements and joints, as well
as changes in the joint coordinates. Solution procedures are developed for the most
challenging problem where the number of degrees of freedom is changed.
In Chapter 10 we develop procedures for calculating the response derivatives with
respect to design variables for designs where results of exact analysis are not available.
Accurate derivatives can be obtained for such designs with a reduced computational
effort.
Nonlinear reanalysis is discussed in Chapter 11. The unified approach presented is
most suitable for solving efficiently the updated linear equations in such problems.
Vibration reanalysis by the unified approach is developed in Chapter 12. Solutions
are demonstrated for problems of eigenvector reanalysis, where we evaluate the mode
shapes, and eigenvalue reanalysis, where we calculate the eigenvalues.
Download
*
SOLID MECHANICS AND ITS APPLICATIONS
Volume 95
Series Editor: G.M.L. GLADWELL
Department of Civil Engineering
University of Waterloo
Waterloo, Ontario, Canada N2L 3GI
Aims and Scope of the Series
The fundamental questions arising in mechanics are: Why?, How?, and How much?
The aim of this series is to provide lucid accounts written by authoritative researchers
giving vision and insight in answering these questions on the subject of mechanics as it
relates to solids.
The scope of the series covers the entire spectrum of solid mechanics. Thus it includes
the foundation of mechanics; variational formulations; computational mechanics;
statics, kinematics and dynamics of rigid and elastic bodies: vibrations of solids and
structures; dynamical systems and chaos; the theories of elasticity, plasticity and
viscoelasticity; composite materials; rods, beams, shells and membranes; structural
control and stability; soils, rocks and geomechanics; fracture; tribology; experimental
mechanics; biomechanics and machine design.
The median level of presentation is the first year graduate student. Some texts are monographs
defining the current state of the field; others are accessible to final year under-
graduates; but essentially the emphasis is on readability and clarity.
Design-Oriented
Analysis of Structures
A Unified Approach
by
URI KIRSCH
Technion,
Israel Institute of Technology, Haifa, Israel
Department of Civil Engineering
TECHNION – Israel Institute of Technology
Haifa, Israel
Preface
This book was developed while I was teaching graduate courses on analysis, design and
optimization of structures, in the United States, Europe and Israel. Structural analysis is
a main part of any design problem, and the analysis often must be repeated many times
during the design process. Much work has been done on design-oriented analysis of
structures recently and many studies have been published. The purpose of the book is
to collect together selected topics of this literature and to present them in a unified
approach. It meets the need for a general text covering the basic concepts and methods
as well as recent developments in this area. This should prove useful to students,
researchers, consultants and practicing engineers involved in analysis and design of
structures. Previous books on structural analysis do not cover most of the material
presented in the book.
The book deals with the problem of multiple repeated analyses (reanalysis) of
structures that is common to numerous analysis and design tasks. Reanalysis is needed
in many areas such as structural optimization, analysis of damaged structures, nonlinear
analysis, probabilistic analysis, controlled structures, smart structures and adaptive
structures. It is related to a wide range of applications in such fields as Aerospace
Engineering, Civil Engineering, Mechanical Engineering and Naval Architecture.
In a typical structural design process, the analysis must be repeated numerous times
due to changes in the size of elements, the material properties, the geometry of the
structure (coordinates of joints), the topology (number and orientation of elements and
joints) and support conditions. The high computational cost involved in repeated
analyses is one of the main obstacles in the solution of structural optimization problems,
and only methods that do not involve many time consuming analyses are useful. In
structural damage analysis, it is necessary to analyze the structure for various changes.
It is difficult to determine a priori what damage scenarios should be checked, and
numerous analyses are required to evaluate various hypothetical scenarios. In nonlinear
analysis the set of updated linear equations must be solved repeatedly many times
during the solution process.
Design-oriented analysis is intended for efficient and accurate repeated analyses of
structures. The book introduces effective computational procedures for reanalysis. The
necessary background material on structural analysis needed in the rest of the book is
summarized in the first two chapters. However, the reader is expected to be familiar
with the basic concepts of matrix analysis of structures. Various analysis models are
considered in the book, including linear and nonlinear analysis, eigenproblems and
design sensitivity analysis. The text does not present a survey on reanalysis methods.
Rather, part 1 concentrates on various concepts and methods that form the basis of the
unified approach presented in part 2. To clarify the presentation, many illustrative
examples and numerical results are demonstrated. No specific system of units is used in
the examples, However, in some examples actual dimensions of the structure and
specified magnitude of forces have been used.
In part 1 (Chapters 1–6) t he basic concepts of design-oriented analysis are introduced
and various reanalysis methods are developed. In part 2 (Chapters 7–12) the concepts
and the methods presented in part 1 are integrated into a unified approach for effective
reanalysis of structures. Recent developments and applications in this area are discussed
in this part of the book. Some sections of the book are necessary for continuity, while
others are needed only for those interested in greater depth in a particular topic. Many
sections are independent and can be omitted, or their order can be changed.
The approach presented in the book is suitable for a wide range of applications. It
combines several advantages in terms of generality, ease-of implementation, flexibility,
efficiency and accuracy. The approach is suitable for various types of changes in the
structure and different types of structures. The solution procedure uses the stiffness
analysis formulation and it can be integrated into available finite element programs.
Calculation of derivatives is not required, and the approach is most attractive in cases
where derivatives are not readily available or not easy to calculate. The accuracy of the
results, and the efficiency of the calculations can be controlled by the level of
simplification and the amount of information considered. Highly accurate results can be
achieved at the expense of more computational effort by considering high-order
approximations. On the other hand, very efficient solutions can be obtained by
simplified low-order approximations. In certain cases exact solutions can be achieved
with a small computational effort.
Chapter 1 presents introductory material on analysis and reanalysis of structures.
Various types of changes in the structure are discussed, including changes in the
structural model itself, and the scope of the text is described.
In Chapter 2 some background material on analysis of structures is introduced.
Linear elastic analysis, analysis of continuum structures, nonlinear analysis and
dynamic analysis are briefly described.
Chapter 3 deals with the statement of reanalysis problems. Formulations of linear,
nonlinear and eigenproblem reanalysis are presented and various direct as well as
approximate reanalysis methods are reviewed.
Direct methods, giving exact closed-form solutions, are presented in Chapter 4.
These methods are efficient in situations where a relatively small proportion of the
structure is changed (e.g., changes in cross sections of only a small number elements).
Chapter 5 presents the most simple and most efficient local approximations. These
include the common Taylor series, the binomial series, simplified first-order
approximations and improved series approximations.
In Chapter 6 we describe global approximations such as polynomial-fitting
techniques, the response surface approach, reduced basis methods and the conjugate
gradient method. These approximations are usually obtained by analyzing the structure
at a number of design points, and they are valid for large changes in the structure.
Chapter 7 presents the combined approximations approach. The basic concepts of
combining various methods into a unified solution approach are introduced. The
advantage is that the efficiency of local approximations and the improved accuracy of
global approximations are combined to obtain effective solution procedures. Some
typical cases, where exact or accurate solutions can be achieved, are developed.
Chapter 8 describes simplified solution procedures that can be derived from the
general approach. The various procedures include approximate and most efficient
techniques as well as direct methods that provide exact solutions. We can view some
conventional approximations and direct methods as particular cases of the general
approach presented.
In Chapter 9 we discuss reanalysis for topological and geometrical changes.
Developing reanalysis methods for such changes is most challenging, since the
structural model itself is changed. Both approximate and exact solutions are
demonstrated for various cases of deletion and addition of elements and joints, as well
as changes in the joint coordinates. Solution procedures are developed for the most
challenging problem where the number of degrees of freedom is changed.
In Chapter 10 we develop procedures for calculating the response derivatives with
respect to design variables for designs where results of exact analysis are not available.
Accurate derivatives can be obtained for such designs with a reduced computational
effort.
Nonlinear reanalysis is discussed in Chapter 11. The unified approach presented is
most suitable for solving efficiently the updated linear equations in such problems.
Vibration reanalysis by the unified approach is developed in Chapter 12. Solutions
are demonstrated for problems of eigenvector reanalysis, where we evaluate the mode
shapes, and eigenvalue reanalysis, where we calculate the eigenvalues.
Download
*
