What Is a Resistor Network?

Experimental stress analysis method, a method of analogy. Related comparison methods include film comparison, electricity comparison, and sand pile comparison.

Experimental stress analysis method, a method of analogy. Related comparison methods include film comparison, electricity comparison, and sand pile comparison.

Chinese name

Resistance network analogy

Foreign name

resistance network analogy

- Introduction to resistance network comparison -resistance network comparison and electricity comparison

In the electrical comparison, consider a cell ABCD of the conductive plate (or electrolytic cell). If the current flowing through the boundary around the cell is I _t , I ₂ , I ₃ , I ₄ (Figure 2), the potential distribution in the conductive plate Described by Laplace's equation: ^[1]

Figure 2 Current flowing through the conductive plate ABCD unit

(1)

As shown in Figure 3, if another current I _j is input on the surface of the cell, the right side of equation (1) is no longer equal to zero, but equal to- I _j , so it can be described by the following Poisson equation:

Figure 3 Input constant current Ij on the surface of the ABCD unit

, (2)

Where U ( x , y ) is a potential distribution function; is the resistivity of the conductive medium; I _j is the applied current. Therefore, as long as the boundary shape of the conductive plate (or electrolytic cell) is kept similar to the shape of the simulated object. A potential proportional to the known boundary value is added to the edge. It can be used to simulate a wide range of mechanical problems described by these two equations. Of course, in the case of Poisson's equation, it is necessary to input a constant current inside the boundary of the conductive plate (or electrolytic cell) (it is equivalent to the lateral load p per unit area added when the film is compared).

The resistance network analogy is to replace the conductive medium with a network of discrete resistors to simulate the phenomenon described by Laplace's equation and Poisson's equation. In addition, a resistance network can be designed to represent the stress or strain of various elastic structures.

Resistance network analogy

The resistor network shown in Figure 1 is a two-layer network interconnected. The resistance between each two adjacent nodes is R. When a current is passed from one or some nodes, each resistance has a certain current distribution, so that there is a certain voltage distribution between each two nodes. Simulate the mechanical problems described by the biharmonic equation. For example, when a plate is loaded in its own plane, its stress state can be described by the following double harmonic equation:

(3)

Where (x, y) is the Airy stress function. If the current is input to the internal nodes of the upper layer network, the problems of the board under lateral loading can be simulated:

(4)

Where w (x, y) is the transverse deflection function of the plate, and p is the load per unit area;

D = Et / 12 (1-v ² ), (5)

Where t is the thickness of the plate and v is the Poisson's ratio.

Resistance network analog application

The resistance network method can also be used to simulate the slope-deflection equations of beams and trusses, and to study wind loads and subsidence stresses in frames. Beam and plate vibration and transient stress.