# US 2020/0401745 A1 · Structure analyzing method, device, and non-transitory computer-readable medium

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- Number: US 2020/0401745 A1
- Document ID: US20200401745A1
- Status: Published application
- Kind: A1
- Application number: 16/687,806
- Filed: 2019-11-19
- Published: 2020-12-24
- Earliest claimed: 2019-06-19
- Assignees: National Central University
- Applicants: National Central University
- Inventors: Tzu-Ying LEE; Wen-Hsiao HUNG; Kun-Jun CHUNG; Hao CHANG
- Web page: https://patentgrep.com/patent/US20200401745A1

## CPC

- G06F 30/23: using finite element methods [FEM] or finite difference methods [FDM]
- G06F 2111/10: Numerical modelling
- G06F: ELECTRIC DIGITAL DATA PROCESSING (computer systems based on specific computational models G06N)

## Abstract

The present invention relates to a structure analyzing method, characterized in that a computer is configured to execute a process, including steps of establishing a spatial-temporal discrete governing model for a discontinuous nonlinear structure based on a finite element analysis, in which the spatial-temporal discrete governing model includes an equivalent nodal secant damping coefficient and an equivalent nodal secant stiffness coefficient at current time step; repeatedly calculating until convergence a secant damping coefficient slope and a secant stiffness coefficient slope based on known parameters, the known equivalent nodal secant damping coefficient and the known equivalent nodal secant stiffness coefficient at previous time step through a computer iteration algorithm; and replacing the equivalent nodal secant damping coefficient and the equivalent nodal secant stiffness coefficient by the converged secant damping coefficient slope and the converged secant stiffness coefficient slope acting as initial values for the next time step.

## Claims

### Claim 1

A structure analyzing method, characterized in that a computer is configured to execute a process, comprising:
establishing a spatial-temporal discrete governing model comprising an equivalent nodal secant damping coefficient and an equivalent nodal secant stiffness coefficient at a current time step for a discontinuous nonlinear structure based on a finite element analysis;
repeatedly calculating until convergence a secant damping coefficient slope and a secant stiffness coefficient slope based on known parameters, the known equivalent nodal secant damping coefficient and the known equivalent nodal secant stiffness coefficient at a previous time step through a computer iteration algorithm performed by the computer; and
replacing the equivalent nodal secant damping coefficient and the equivalent nodal secant stiffness coefficient by the converged secant damping coefficient slope and the converged secant stiffness coefficient slope acting as initial values for a next time step.

### Claim 2 (depends on 1)

The structure analyzing method as claimed in claim 1, wherein the process further comprises:
discretizing the discontinuous nonlinear structure into a plurality of spatial elements and establishing the spatial-temporal discrete governing model for each of the plurality of spatial elements;
applying an equivalent Rayleigh damping to the spatial-temporal discrete governing model to form a second spatial-temporal discrete governing model; and
applying the known equivalent nodal secant damping coefficient and the known equivalent nodal secant stiffness coefficient at the previous time step to form a third spatial-temporal discrete governing model comprising the equivalent nodal secant damping coefficient and the equivalent nodal secant stiffness coefficient.

### Claim 3 (depends on 1)

The structure analyzing method as claimed in claim 1, wherein the spatial-temporal discrete governing model, the second spatial-temporal discrete governing model, and the third spatial-temporal discrete governing model are defined by equations as follows:
Mt+ΔtÜ(r)+Ct+Δt{dot over (U)}(r)+t+ΔtKT(r-1)ΔU(r)=t+ΔtR−t+ΔtFS(r-1),
wherein (r) represents the r times iteration, M is the mass matrix, C is the damping matrix, t+ΔtKT(r-1) is the tangent stiffness matrix after the (r−1) times iteration, R is the external force vector, t+ΔtFS(r-1) is the internal force vector for an element node, Ü and {dot over (U)} are the acceleration vector and the velocity vector for a node respectively, and ΔU(r) is the incremental displacement vector for the r times iteration; and
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wherein C=a0M+a1KI is the equivalent Rayleigh damping, KI is the structure initial stiffness, a0 and a1 are constants Δ{dot over (U)}i(r) and ΔUi(r) are the incremental velocity vector and the incremental displacement vector for the r times iteration respectively, t+Δt(FkD)i(r-1) is the element node damping force vector for the previous iteration considering stiffness-proportional damping a1KI, t+Δt(FkD)i(r-1) is the element node internal force vector for the previous iteration, t+Δt({tilde over (C)}sec)i(r-1) and t+Δt({tilde over (K)}sec)i(r-1) are the equivalent node secant damping coefficient and the equivalent node secant stiffness coefficient respectively.

### Claim 4 (depends on 1)

The structure analyzing method as claimed in claim 1, wherein the equivalent node secant damping coefficient and the equivalent node secant stiffness coefficient are defined by equations as follows:
t+Δt({tilde over (C)}sec)i(r-1)Δ{dot over (U)}i(r-1)≡Δt+Δt(FkD)i(r-1) and t+Δt({tilde over (K)}sec)i(r-1)ΔUi(r-1)≡Δt+Δt(FS)i(r-1),
wherein the Δt+Δt(FkD)i(r-1) and Δt+Δt(FS)i(r-1) are the element incremental stiffness-proportional damping force and the element internal force respectively for the previous iteration.

### Claim 5 (depends on 1)

The structure analyzing method as claimed in claim 1, wherein the discontinuous nonlinear structure is a discontinuous yielded structure, a discontinuous collapsed structure, a discontinuous cracked structure, a discontinuous damaged structure, a discontinuous fallen structure, a discontinuous failed structure, or a discontinuous separated structure.

### Claim 6 (depends on 1)

The structure analyzing method as claimed in claim 1, wherein the computer iteration algorithm is a quasi-Newton iteration method, or a secant method.

### Claim 7

A structure analyzing device, characterized in that a hardware processor is configured to implement a process, comprising:
establishing a spatial-temporal discrete governing model comprising an equivalent nodal secant damping coefficient and an equivalent nodal secant stiffness coefficient at a current time step for a discontinuous nonlinear structure based on a finite element analysis;
repeatedly calculating until convergence a secant damping coefficient slope and a secant stiffness coefficient slope based on known parameters, the known equivalent nodal secant damping coefficient and the known equivalent nodal secant stiffness coefficient at a previous time step through a computer iteration algorithm performed by the hardware processor; and
replacing the equivalent nodal secant damping coefficient and the equivalent nodal secant stiffness coefficient by the converged secant damping coefficient slope and the converged secant stiffness coefficient slope acting as initial values for a next time step.

### Claim 8 (depends on 7)

The structure analyzing device as claimed in claim 7, wherein the process further comprises:
discretizing the discontinuous nonlinear structure into a plurality of spatial elements and establishing the spatial-temporal discrete governing model for each of the plurality of spatial elements;
applying an equivalent Rayleigh damping to the spatial-temporal discrete governing model to form a second spatial-temporal discrete governing model; and
applying the known equivalent nodal secant damping coefficient and the known equivalent nodal secant stiffness coefficient at the previous time step to form a third spatial-temporal discrete governing model comprising the equivalent nodal secant damping coefficient and the equivalent nodal secant stiffness coefficient.

### Claim 9

A non-transitory computer-readable medium storing a program causing a computer to execute a process, comprising:
establishing a spatial-temporal discrete governing model comprising an equivalent nodal secant damping coefficient and an equivalent nodal secant stiffness coefficient at a current time step for a discontinuous nonlinear structure based on a finite element analysis;
repeatedly calculating until convergence a secant damping coefficient slope and a secant stiffness coefficient slope based on known parameters, the known equivalent nodal secant damping coefficient and the known equivalent nodal secant stiffness coefficient at a previous time step through a computer iteration algorithm performed by the computer; and
replacing the equivalent nodal secant damping coefficient and the equivalent nodal secant stiffness coefficient by the converged secant damping coefficient slope and the converged secant stiffness coefficient slope acting as initial values for a next time step.

### Claim 10 (depends on 9)

The non-transitory computer-readable medium as claimed in claim 9, wherein the process further comprises:
discretizing the discontinuous nonlinear structure into a plurality of spatial elements and establishing the spatial-temporal discrete governing model for each of the plurality of spatial elements;
applying an equivalent Rayleigh damping to the spatial-temporal discrete governing model to form a second spatial-temporal discrete governing model; and
applying the known equivalent nodal secant damping coefficient and the known equivalent nodal secant stiffness coefficient at the previous time step to form a third spatial-temporal discrete governing model comprising the equivalent nodal secant damping coefficient and the equivalent nodal secant stiffness coefficient.