Introduction
Implications of the Kirchhoff hypothesis
Part
1
introduction
background
Fibers reinforced materials are most frequently used by employing multiple layers of material to form a laminate. Following instructions: 1. Each layer may have a different fiber orientation. 2. Some layers may use graphite fibers ,while others may use glass fibers. 3. The number of layers that make up laminates may be different. 4. There are differences in fiber angles and the arrangement of layers. The reason is the arrangement : The first is [0/90/90/0]������ The second is [90/0/0/90]������
Because before deformation the plate is flat and the layer interfaces are parallel to each other and to
the geometric mid-plane of the
plate, line AA’ is normal to each interface.
It is of prime concern to understand how changing these variables influence laminate response and structural response .
The ultimate purpose is to be able to design laminates so that structures have a specific response, so that deformation are within certain limits and stress levels are below a given level.
How changing material properties in a group of layers changes response
第6 页
focus point
The magnitude and character of the load
The dependent factors of stress
When the stacking sequence involves adjacent layers of opposite orientation, short hand notation is used.
When a stacking sequence is a subset consisting of several layers is repeated, further shorthand notation is used.
第 15 页
Part
3
Implications of the Kirchhoff hypothesis
implications
We should stress that no mention has been made of material properties. If we accept the validity of the Kirchhoff hypothesis, then we assume that it is valid for the wide range of material properties that are available with fiber-reinforced composite material.
第5 页
focus point
How the fiber angles of the individual layers influence laminate response
How laminates the stacking arrangement of the layers influences the response
第8 页
Laminate nomenclature
Two requires: First, we have a method of describing a laminate, particularly the fiber orientation of each layer . second, we must establish a coordinate system for specifying locations through the thickness, along the length, and across the width of the laminate.
Extend in the z direction from – H/2 to +H/2 The locations of the layer interfaces are denoted by a subscripted z . The kth layer by ������������−������ and ������������ .
direction of the laminate. The distance between
point t and t' in figure, then, is the same as the distance between t and t' in figure, According to this hypothesis, there is no through-thickness.
change length.
The normal line does
not deform
第 14 页
content
The normal of the above figure has rotated and translated due to the deformation caused by the applied loads . That the line doer not change length is another important part of the assumption. For the length of the line to remain unchanged, the top and bottom surfaces of the laminate must remain the same distance apart in the thickness
To identify the fiber angles of the various layers, the fiber angle relative the +x axis of each layer is specified
第9 页
Laminate nomenclature
To indicate the total stacking, we need to use a subscript T. The laminate is symmetric, the stacking notation can be abbreviated by referring to only one-half of it and subscripting the notation with the symbol S.
第 11 页
Part
2
The Kirchhoff hypothesis
2-1 研究思路
2-2 研究方法 2-3 可行性说明
content
Line AA’ is straight and normal to the laminate’s geometric mid-surface, and passes through the laminate
Composite Materials
Chapter 6 hypothesis 课件组员：
Classical lamination theory : the Kirchhoff
目录
CONTENTS
Laminate strains
The Kirchhoff hypothesis Laminate stresses
第 10 页
essentials
This chapter will introduce simplifications in the analysis of fiberreinforced composite materials that will allow us to obtain answers for a large class of problems. we can thus evaluate the influence of fiber directions, stacking arrangements, material properties, and so forth, on laminate and structural response .the simplified theory is called classical laminate theory.
第 17 页
summary
The displacements of an arbitrary point P with coordinate(x, y, z) is given by : ������������ ������ (������, ������) ������ ������, ������, ������ = ������ ������, ������ − ������ ������������