How to solve the statically indeterminate problem in material mechanics? The deformation of statically indeterminate members is linear with the load, because the classical theory of isotropic materials and uniform stress is established, which is similar to the micro-deformation theory and the actual deformation, which has been verified by engineering practice.
If it is statically indeterminate, the deformation of the bar must be nonlinear with the load; Because its constraint position is uncertain.
In mechanics of materials, how to judge the number of statically indeterminate (1) once statically indeterminate?
(2) statically indeterminate state
(3) Three times statically indeterminate
In fact, it is to see that you have become a statically indeterminate structure after removing several constraints, so he is statically indeterminate several times.
I don't understand.
How to solve the statically indeterminate problem of material mechanics with matlab, and how to solve the statically indeterminate problem of material mechanics with matlab. The solution idea is to decompose statically indeterminate structure beam (truss) into several finite elements by using the principle of finite element method, and establish the relationship between force and displacement of each element, then connect each element through nodes, and the force between each element is transmitted through nodes, thus establishing the relationship between force and displacement of the whole structure, simplifying the problem into a matrix calculation problem, and then programming by using mathematical software matlab.
The specific solution steps can be carried out according to the following methods:
1, according to the principle of element division, divide the structure into several parts;
2, element analysis, write the rigid matrix of the element (expressed in matrix form);
3. Synthesize all elements, and form a total rigid array [K], a total external force array {F} and a total displacement array of the structure according to the node displacement serial numbers.
{ QR }； Simplify the matrix according to the boundary conditions;
4. Solve the deformation of each node from {qr}=inv([K]r)*{Fr}; ? %inv([K]r) is the inverse of [K]r.
5. From {F}=[Kz] {q}, the reaction force of each node can be obtained.
6. According to the above requirements, the matlab program for solving statically indeterminate mechanical problems is designed.
For more information, please refer to this document and website links.
How to judge the number of statically indeterminate unknowns-the number of equations in material mechanics?
For example:
A beam with one end fixed and one end simply supported.
Unknown quantity 5 (fixed support 3+ simply supported 2)-3 (force balance equation in two directions+moment balance equation) =2.
Mechanics of Materials The mechanics of statically indeterminate rigid frames is an independent basic discipline, which involves the mechanical properties of force, motion and medium (solid, liquid and gas are Satan and plasma), macro, micro and micro, and studies the phenomenon with mechanical motion as the main body and its coupling with physical, chemical and biological motion. Mechanics is not only a basic discipline, but also a technical discipline. It studies energy and force and their relationship with the equilibrium, deformation or motion of solids, liquids and gases. Mechanics can be roughly divided into three parts: statics, kinematics and dynamics. Statics studies the balance of forces or the static problems of objects. Kinematics only considers how an object moves and does not discuss its relationship with force; Dynamics discusses the relationship between the motion of an object and the force it receives. The establishment and use of modern mechanical experimental devices such as large wind tunnels and water tunnels is a comprehensive scientific and technological project, which requires the cooperation of many types of work and disciplines.
Thoughts on solving statically indeterminate problems by moment distribution method
(1) Calculate the bending moment of the fixed end.
That is, Mba and Mab on page 282 when there is external force.
(2) Find the distribution coefficient and then the distribution torque.
I = ei/a. (linear stiffness)
Rotational stiffness S=4i (distal fixation)
S=3i (simply supported at the far end)
S=i (distal sliding)
S=0 (remote idle)
Distribution coefficient p 1(Mba direction) =S 1/(S 1+S2) (when the node has two rods)? p2？ (Mbc direction) =S2/(S 1+S2) (right) B is the node.
Note: P 1+P2= 1? P 1+P2+P3= 1 (in the case of three strokes)? B is a node.
Distribution torque:
If it is node B (MBA+MBC) * (-1) * p1= MBA'
? (Mba+MBC)*(- 1)* p 1 = MBC '
(3) transfer coefficient transfers torque
B is a node.
A C end fixing C=0.5
?
A C end sliding C=- 1
?
Ac terminal freedom C=0
Reverse transfer torque =C* distribution torque
(4) Find the final bending moment of the rod end.
? Bending moment at rod end = bending moment at fixed end+distributed moment (or transmitted moment (directly adding distributed moment and other transmitted moments at node B)) (single node case)
Find a statically indeterminate stress problem and solve it without a diagram, boy! "Stress statically indeterminate"? Is it "the internal force is statically indeterminate"
However, there are many books and examples for solving statically indeterminate problems in mechanics of materials, which can be understood by reading.
How to judge whether the structure changes or not and how to judge the number of statically indeterminate times in material mechanics? Good method! According to the rule of three rigid plates and two rigid plates, this will be discussed in the first chapter of structural mechanics.
Write the calculation steps of solving statically indeterminate problems by force method 1. According to the constraint conditions of the structure, determine how many times of statically indeterminate.
2. According to the constraint conditions (x, y, rotation angle), the deformation compatibility equations (i.e. ∑x=0, ∑y=0, ∑M=0) are listed respectively, in which the displacement of material mechanics is the topic.
3. Solve the surplus force of each constraint condition separately.
4. Substitute various forces into the calculation diagram to solve the internal forces and nodal forces of each component of the structure respectively.
5. Draw an internal force diagram