A theory of latticed plates and shells / G.I. Pshenichnov.

Format:

Book

Author/Creator:

Pshenichnov, G. I.

Series:

Series on advances in mathematics for applied sciences ; v. 5.

Series on advances in mathematics for applied sciences ; vol. 5

Language:

English

Subjects (All):

Elastic plates and shells.

Elastic solids.

Physical Description:

1 online resource (324 p.)

Other Title:

Latticed plates and shells

Latticed plates and shells.

Place of Publication:

Singapore ; New Jersey : World Scientific, 1993.

Language Note:

English

Summary:

The book presents the theory of latticed shells as continual systems and describes its applications. It analyses the problems of statics, stability and dynamics. Generally, a classical rod deformation theory is applied. However, in some instances, more precise theories which particularly consider geometrical and physical nonlinearity are employed. A new effective method for solving general boundary value problems and its application for numerical and analytical solutions of mathematical physics and reticulated shell theory problems is described. A new method of solving the shell theory's nonli

Contents:

PREFACE; CONTENTS; CONSISTENTLY USED SYMBOLS; Chapter 1 RETICULATED SHELL THEORY: EQUATIONS; 1.1 Anisotropic Shell Theory: Basic Equations; 1.1.1 Static equations; 1.1.2 Geometric equations; 1.1.3 Constitutive equations for anisotropic shells; 1.2 Constitutive Equations in the Reticulated Shell Theory; 1.2.1 Constitutive equations for the rods of reticulated shells; 1.2.2 Constitutive equations for a calculation model; 1.2.3 Assessment of the deformation components and forces in the rods using the forces and moments of the calculation model

1.2.4 Constitutive equations for an oblique-angled system of coordinates1.2.5 More complex version of the constitutive equations; 1.2.6 Study of the geometrical stability of the reticulated shell's calculation model. Deformation energy; 1.2.7 Boundary conditions; 1.3 More Precise Constitutive Equations in the Reticulated Shell Theory; 1.3.1 Allowance for transverse shear, cross-section warping and transverse deformation of rods; 1.3.2 Allowance for the rods' non-linear-elastic deformation; Chapter 2 DECOMPOSITION METHOD

2.1 Solution of Equations and Boundary Value Problems by the Decomposition Method2.1.1 Decomposition method; 2.1.2 Merits of the method; 2.2 Application of the Decomposition Method for Particular Problems; 2.2.1 Analytical solutions; 2.2.2 Numerical solutions; Chapter 3 STATICS; 3.1 Plane Problem; 3.1.1 A plate with more than two families of rods; 3.1.2 A plate with two families of rods; 3.2 Bending of Plates; 3.2.1 Differential equation for bending; 3.2.2 A plate with a rhombic lattice; 3.2.3 A plate with more than two families of rods; 3.2.4 Plates with an elastic contour

3.2.5 Plates made from composite material3.2.6 Plates made from nonlinear elastic material; 3.2.7 Bending of plate subjected to large deflections; 3.3 Shallow Shells; 3.3.1 Various differential equation systems for shallow shells subjected to medium bending; 3.3.2 Shallow shells with constant lattice parameters; 3.3.3 Shallow spherical shells; 3.4 Small Parameter Method in the Shallow Shell Theory; 3.4.1 Constitutive equations; 3.4.2 Differential equation system; 3.4.3 Small parameter method; 3.4.4 Numerical method for solving boundary iteration process problems

3.4.5 Shallow non-circular cylindrical shells3.5 Circular Cylindrical Shells; 3.5.1 Differential equation system; 3.5.2 Cylindrical shell with a rhombic lattice; 3.5.3 Cylindrical shell with a square lattice; 3.5.4 Calculation tables for reticulated cylindrical shells; 3.6 Optimum Design of a Shell with an Orthogonal Lattice; 3.6.1 Statement of problem; 3.6.2 Solution using the optimal control theory; 3.7 Shells of Rotation; 3.7.1 Basic relationships and equations; 3.7.2 Axisymmetrical deformation; 3.7.3 Non-axisymmetrical deformation; 3.7.4 Cylindrical shell made from composite material

3.7.5 Shell of rotation made from nonlinear elastic material

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9789812797100

9812797106

9781615838707

1615838708