OpenSES A user interface for structural dynamics and teaching earthquake engineering

Graphic user interface structure

The graphic user interface (GUI), which was developed in this study, includes two main components, each of which is designed to meet the specific analytical needs. The first component, dedicated to one degree of freedom systems (SDOF), works to benefit from Matlab libraries to solve regular differential equations and represents a dynamic response to the system. The second component, designed for 3D frame analysis (3D), works as a tool before processing and post -therapist for Opensees as shown Figure 1, the streamlined plan for the second component, which lacks its nature to a graphical interface. During the pre -processing stage, the graphic user interface facilitates the definition of simplified modeling parameters, treats these inputs, and automatically creates the corresponding modeling code. In the post -processing stage, the graphic user interface only enables users to visualize the results of the analysis through graphic outputs, but also facilitates a deeper understanding of structural behavior by providing time conspiracies of time of displacement, speed, acceleration, basic powers and endurance forces. These perceptions help users to identify peak responses, evaluate the effectiveness of seismic isolation systems, and explain the dynamic behavior of structures under different loading conditions. By converting the initial numerical data to interpretable graphic fees, the graphic user interface blocks the gap between mathematical results and engineering insight, thus enhancing the user's ability to evaluate structural performance under investigation critically.

Figure. 1Single Freedom Systems degree (SDOF)

SDOF systems act as prominent tools to clarify the basic principles in the world of structural dynamics. These systems consist of three basic ingredients: cut block (M), spring stiffness (K), and tinyid (C). The ruling equation of the SDOF movement is expressed by EQ. 123.

$$ m \ ddot {u} \ left (t \ right) + C \ dot {u} \ left (t \ right) + ku \ left (t \ right) = f \ left (t \ right) $$

(1)

When the block displacement is indicated by U (T), the speed by \ (\ dot {u} \ left (t \ right) \), acceleration by \ (\ ddot {u} \ left (t \ right)), and external download by F (T). It is worth noting that when the external load F (T) is empty, the SDOF system is subject to free vibration, which is started by displacement or the speed of the initial mass. On the contrary, forced vibration describes the dynamic response to the system when exposed to external load F (T). SDOF systems are categorized with energy dispelling as diluted systems, characterized by a positive damping factor, c.

This specified part of the GUI is placed to support students in understanding the dynamic response to both the covered SDOF systems and not covered by forced and free vibrations. Figure 2 shows a screenshot of the SDOF GuI, which provides visual representation of its appearance and functions.

Figure 2

One degree of Freedom Graphic user interface.

Although SDOF systems act as basic tools in teaching structural dynamics, it is important to identify their restrictions in the representation of real structures. In practice, the SDOF model is close to the dynamic response of the structure by placing it perfectly as a severed mass system with written and diverting hardness, governed by one equation for movement. This simplification is especially effective for buildings or low -height structures as the first vibration mode dominates the total response. It provides an insight into the basic dynamic behavior such as free vibration, and the hygiene, ringing, damping effects, and the effect of loading properties.

However, SDOF models have inherent restrictions when used to represent actual structures. They neglect high -status contributions, which are decisive in the seismic response of medium buildings to tall and irregular formations. The effects of sprains, changes in the distribution of mass and hardness cannot be captured, and structural violations in the plan or height by bringing SDOF. In addition, the model assumes a uniform response through the high structure and cannot simulate damage to the level of the element, or flexible behavior, or the effects of interaction between the various structural components. Therefore, while SDOF systems are valuable for preliminary studies and to verify the health of the most complex models, they are not enough for detailed seismic evaluation or performance -based design for real structures. More comprehensive models, such as MDOF models or limited elements, are necessary to accurately assess structural behavior within the framework of realistic download scenarios.

The date of the linear time of the tires

The Lotha Time Date Analysis Component (LTHA) was developed for the GUI in Figure 3 specifically to facilitate media analysis and the linear time analysis of three -dimensional cutting frames. Users can identify individual flooring blocks within the frame by introducing values ​​for distributed dead loading and direct loading. After that, the graphic user interface uses these specific ground fans, along with the approximate basic vibration period of the structure (referred to as T1), to devise the hardening of each mathematical story. This account is made through the reverse application of the B method, as is described in ASCE 7-1624. Moreover, the graphic user interface includes the ability to integrate seismic insulation bearings into the structural model. In this context, the metal structure is treated as a linear flexible system, while it is assumed that the ingredients associated with the seismic insulation system show an uncontrolled behavior.

Figure 3

Linear time analysis Analysis of the graphic user interface.

Mitod

According to the B methods, the side -floor side -floor account can be performed for the EQ cutting structure. 225, which is represented as follows:

Tream / right) $$

(2)

where,

\ (w_ {x} \): The seismic weight in the ground x.

\ (H \): the height of the word x.

\ (w {i} \): The seismic weight in the floor I.

\ (H \): the height of the word i.

\ (V \): Copy the total rule.

The relative displacement can be determined between the first levels and I-1 using EQ. 325, where it is the side hardness at the first level.

$ thread

(3)

Horizontal displacement can be calculated for the base using EQ. 425.

$ thread

(4)

Side Story Molstate can be calculated with EQ. 525, provided that all stories have the same stiffness of the story.

$$ k_ {i} = \ frac {{4 \ pi^{2} w \ mathop \ sum \ noimits_ {i = 1}^{n} \ delta_ {i}^{2}}} {g t_ {1}} 1^{n} \ delta_ {i} f_ {i}}}}} $$

(5)

Special analysis

Eigen analysis, also known as a conditional analysis, is a widely used methodology in assessing vibrational properties in structural systems. EIGEN analysis results serves the purpose of separating multi -degree systems movement equations, allowing the analysis approach that treats the structural system as a group of one -class systems. This technology assumes a pivotal role as an essential stage in the dynamic analysis of structural systems, and includes both areas and frequency. Eigen is used within Opensees to perform Eigen analysis.

Analyzing the date of the linear time

Time date analysis is used to calculate the dynamic response to the structures exposed to dynamic loading, including seismic excitement in the time field. In the context of analyzing the history of the linear time, it is assumed that the structural system offers a flexible written response. Non -physical lineage is absorbed by using equivalent linear properties. On the contrary, the analysis of the non -linear time date takes into account the non -linear characteristics of the structure, as response parameters such as displacement and internal forces are calculated each time using numerical techniques such as the NewMark -Beta method.

NewMark – Beta method is a numerical method widely used to solve differential equations in assessing the dynamic response to structural systems in time field 23

cover

(6)

Where it represents the displacement, it represents \ (\ dot {u} \) and \ (\ ddot {u} \) speed and acceleration as a function of time, respectively. M is the block matrix, C is a damping matrix, and K is a solid matrix. F is the strength of external excitement (dynamic loading) as a time function. The first covered indicates the time step number. The movement equation is between two steps of time (I and I + 1) in EQ. (7) 23. The parameters β and γ are used as weights in the acceleration approximation.

$$ \ Delta M \ Ddot {u} \ left ({t_ {i}} \ right) + \ Delta C \ dot {u} \ left ({t_ {i}} \ right + \ Delta ku \ left ({i {i}} \ right) $$

(7)

Using the newmark equation, ((Delta \ Dot {u} _} \) and (\ Delta u {i} \) is calculated using EQS. (8) and (9), respectively 23.

$$ \ Delta \ Dot {u} _ {i}[ {\left( {1 – \gamma } \right)\Delta t} \right]”

(8)

and

$ thread[ {\left( {0.5 – \beta } \right)\left( {\Delta t} \right)^{2} } \right]\ dot {u} _ {i} + [\beta \left( {\Delta t)^{2} } \right]\ dot {u} _ {i + 1}}} $$

(9)

EQ simplify. (9) Equipment yield. (10) 23.

$$ \ Delta u {i} = \ left ({\ delta t} \ right) \ dot {u} _ {i} + \ frac {{\ left ({\ delta t} \ right^{2}}} {2} t)^{2}} \ Delta \ ddot {u} {i} $$

(10)

A solution for ((Delta \ Ddot) {u} _ {i} \) 23

$ thread

(11)

By replacing \ (\ Delta \ ddot {u} _ {i} \) in the equation of (\ delta \ dot {u} _ {i}} \)

\ Frak {\ gamma} {2 \ beeta} \ right) \ Ddot {u} _ {i} $$

(12)

You can calculate \ (\ delta u_ {i} \) after replacing \ (\ delta \ dot {u} _ {i} \) and \ (\ delta \ ddot {u} _ {i} \) in the movement equation 23,

cover

(13)

$ thread

(14)

where

$ thread

(15)

cover[ {\frac{1}{2\beta }m + \Delta t\left( {\frac{\gamma }{2\beta } – 1} \right)c} \right]\ dot {u} _ {i} $$

(16)

Once you calculate \ (\ delta u_ {i} \), \ (u_ {i + 1}, \ dot {u} _ {i + 1} \; {\ text {and}} \; \ ddot {u} _ i + 1 \))

Dot {u} _ {i} + \ delta \ dot {u} _ {i + 1} $$

(17)

The common value of γ and β is 0.5 and 0.25, respectively. These values ​​are compatible with the fixed intermediate acceleration method, which have the following characteristics:

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