Kirchhoff-Love理论：薄板与壳体的应力变形分析

Plates
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"plates and shells (MIT lecture notes)" 是一份关于薄板与壳体理论的学术资料，主要探讨了在受力和弯矩作用下薄板的应力和变形问题。这份资料由 MIT 提供，涉及的内容包括应变位移关系、构型方程以及用变分法推导平衡方程和边界条件等。 薄板理论，特别是 Kirchhoff-Love 理论，是二维数学模型，用于分析薄板在三维空间中的力学行为。该理论基于 Kirchhoff 的假设，由 Love 在1888年发展完善。理论中，假设可以使用一个中间平面来简化三维薄板为二维形式进行分析。 内容详细展开： 1. 应变位移关系对于薄板的分析至关重要。这部分内容首先介绍了1D应变度量，包括工程应变和Green-Lagrangian应变的概念。接着，详细讨论了3D应变度量，特别提到了如何导出Green-Lagrangian应变张量，并详细规定了薄板的应变位移关系。 2. 构型方程的推导涉及到弯矩和轴向力的定义。这部分讨论了弯矩的能量，包括弯矩的概念、弯矩能量密度以及总弯矩能量。同时，还涵盖了膜能部分，如轴向力、膜能密度和总膜能。 3. 通过变分法开发平衡方程和边界条件是理论的核心部分。在弯曲理论中，详述了薄板的总势能，其第一变分用于找到势能的最小化状态，从而导出平衡方程和边界条件。对矩形板的特殊情况进行了具体说明。此外，还讨论了考虑膜效应的弯曲-膜理论，其总势能和第一变分也得到了阐述。 这份资料不仅涵盖了基本的理论概念，还深入到实际问题的求解方法，对于理解和应用薄板和壳体理论有极大的帮助。对于学习者来说，这是一份全面且深入的学习材料，能够帮助他们掌握薄板在受力情况下的力学行为分析。

Theory of Plates and Shells

2021-06-20 上传
《板壳理论》是斯蒂芬·提莫谢夫（S. Timoshenko）于1959年出版的一本经典著作，由McGraw Hill出版社在纽约发行。这本书是结构工程领域的重要参考资料，主要探讨了薄板和薄壳结构在受力条件下的行为和分析方法。...

Theory and Analysis of Elastic Plates and Shell

2018-04-18 上传
《弹性板壳理论与分析》一书是关于板壳理论的经典著作，作者J.N. Reddy通过对基础理论的详细阐述，带领读者深入理解了从经典板壳理论到剪切板壳理论的各个重要方面。该书不仅涉及理论知识，还提供了实际应用的分析，...

ansys apdl shell

2023-09-15 上传
These shell elements enable users to model various types of shell structures, such as plates, shells, and membranes, and perform simulations to analyze their behavior under different loading ...

主打产品主打产品Alloy Steel Plates，请帮我写4个围绕这个产品和公司实力展开的Google英文创意内容，不超过90字符，请帮我写2个围绕这个产品和公司实力展开的Google英文创意内容，不超过90字符

2023-09-14 上传
1. Superior Strength Alloy Steel Plates - Trust our expertise and experience! 2. Customized Alloy Steel Plates - Precision-engineered for your needs. 3. Top-Quality Alloy Steel Plates - Reliable ...

It is said that in ancient Indian holy temples, there was a game called Hanoi. The game is on a copper plate device with three rods (numbered a, B and C). there are many plates are placed in order from bottom to top and from large to small in rod A. The goal of the game: move all the gold plates on pole A to pole C, and keep the original order. Operating rules: only one plate can be moved at a time, and the large plate is always kept under the three rods and the small plate is on the top. During the operation, the plate can be placed on any rod A, B and C. Solve the above problems with programs, try to propose an optimized algorithm.

2023-06-02 上传
The function first determines the order in which to move the plates based on the parity of `n` and the index of the plate. Then, the function uses a loop to move each plate in the correct order. ...

import cv2 import numpy as np from PyQt5 import QtWidgets from paddleocr import PaddleOCR from yolov8 import YOLOv8 # 假设你有YOLOv8的实现 # 定义车牌定位类 class PlateLocator: def __init__(self, model_path): self.model = YOLOv8(model_path) def locate_and_crop(self, image): boxes = self.model.detect(image) plates = [] for box in boxes: x, y, w, h = box plate = image[y:y+h, x:x+w] plates.append(plate) return plates # 定义车牌识别类 class PlateRecognizer: def __init__(self): self.model = PaddleOCR() def recognize(self, plate): result = self.model.ocr(plate, use_gpu=False) return result # 定义GUI类 class App(QtWidgets.QMainWindow): def __init__(self, locator, recognizer): super().__init__() self.locator = locator self.recognizer = recognizer self.initUI() def initUI(self): # 创建识别按钮 btn = QtWidgets.QPushButton('识别', self) btn.clicked.connect(self.detect_plate) # 其他UI代码... def detect_plate(self): # 从视频流中捕获一帧图像 ret, frame = self.cap.read() # 定位和裁剪车牌 plates = self.locator.locate_and_crop(frame) for plate in plates: # 对车牌进行识别 result = self.recognizer.recognize(plate) print(result) # 展示或保存结果... if __name__ == "__main__": locator = PlateLocator('yolov8_model_path.pth') recognizer = PlateRecognizer() app = QtWidgets.QApplication([]) ex = App(locator, recognizer) ex.show() app.exec_()帮我改进一下代码

2023-06-01 上传
def locate_and_crop(self, image): boxes = self.model.detect(image) plates = [] for box in boxes: x, y, w, h = box plate = image[y:y+h, x:x+w] plates.append(plate) return plates # 定义车牌识别...

besselj(n,beta)

2023-04-06 上传
The Bessel function of the first kind is used in many areas of physics and engineering, such as in the vibration analysis of circular plates and in the modeling of electromagnetic waves in cylindrical...

S. V. Patankar 和 D. B. Spalding 提出了分布阻力的概念，来表征壳程固体表面对流体流动的影响，即把壳程内的换热管束、支撑板以及折流挡板等固体结构看成是多孔介质的骨架，用体积多孔度来表示流体流动所占有的空间占到整个换热器名义空间的百分比，形成了简化的换热器流体流动和传热的数学模型。这种方法既保留了用微分方程来描述壳程流体流动与传热的特点，又简化了换热器的复杂的几何结构，从而实现了管壳式换热器壳程流场的数值模拟。尽管 S. V. Patankar 和 D. B. Spalding 所研究的换热器较简单，网格划分较粗，计算精度也较低，未准确地得到换热管束间的流体流动情况。但是其模拟过程阐述了流动的数值模拟技术，为常用换热器的三维流场数值模拟提供了一定基础。 用另一种语言表示

2023-05-15 上传
They treated the solid structures such as heat transfer tube bundles, support plates, and baffle plates as a porous medium skeleton and used the volume porosity to represent the percentage of space ...

To the best of our knowledge, no research has studied the inversely phased wavy flow fields of anode and cathode in a MBPP structure to investigate the 3D distributions of internal parameters inside the stack. There are two distinguished features of the mentioned design: (1) the wavy flow fields are asymmetric between the anode and cathode sides with a phase deviation of 180◦; (2) the inversely phased wavy coolant channels at the back sides of anode and cathode metallic plates construct the intercrossed two-layered coolant flow fields. In such a complicated 3D geometry of the MBPP stack, the detailed parameter distributions inside the stack should be studied under different operating conditions for the design optimization.

2023-02-10 上传
從目前的研究來看，尚未有研究探索MBPP結構中陽極和陰極之間的反相波浪流場的3D內部參數分佈。該設計有兩個突出的特徵：（1）陽極和陰極之間的波浪流場是不對稱的，其相位差為180°；（2）陽極和陰極金屬板背面的...

用中文翻译：The anode side coolant channels W1 ~ W6 at the upper (solid lines) and lower (dashed lines) layers overlap and interweave, as shown in Fig. 11 (c). In the present model, coolant of the lower layer contact anode metallic plate directly with higher temperature than that of the upper layer. The temperature distribution results show apparent heat exchange effect between the adjacent channels at intersections of the wavy channels, for example, the W1 channel at lower layer and the W2 channel at upper layer. The heat exchange effect of the intercrossed wavy flow field is mainly caused by two thermal processes: the thermal conduction through the coolant material in contact and the thermal convection by the secondary flow induced mass transfer indicated with yellow dashed circles. Fig. 11 (d) and (e) show local temperature of the anode and cathode metallic plates. Due to the fine thermal conductivity, the maximum temperature deviation is less than 1 K. The ribs which contact the MEA directly present apparently higher temperature than the channel compartments. The edge areas show the highest temperature where the local portion of MEA generates reaction heat without coverage by the wavy coolant channels. From the thermal management point of view, the edge area of the wavy flow fields with local hot spot behavior should be concerned when designing the MBPP fuel cell stack.

2023-02-10 上传
热液流道W1~W6上下层（实线和虚线）重叠交错，如图11（c）所示。在当前模型中，下层冷却剂与阳极金属板直接接触，温度比上层高。温度分布结果表明，波浪流道交叉点处相邻流道之间存在明显的热交换效应，例如下层的W1...
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