NX NASTRAN阻尼效应建模解析

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"阻尼效应建模-digital video and hd_ algorithms and interfaces (2nd ed.)" 在《阻尼效应建模-digital video and hd_ algorithms and interfaces (2nd ed.)》中,主要讨论了动力学分析中的阻尼效应及其在NX NASTRAN软件中的应用。阻尼是一种能量损耗机制,它可以是由于内部摩擦、材料的内迟滞效应、接点摩擦或其他非线性效应,例如金属的塑性应变造成的。在工程分析中,理解阻尼对于准确模拟结构的动力响应至关重要。 NX NASTRAN提供了四种类型的阻尼模型:粘滞阻尼、结构阻尼、模态阻尼和非线性阻尼。粘滞阻尼模拟了与速度成比例的力,通常通过CVISC和CDAMPi数据块输入。在瞬态响应分析中,结构阻尼会被转换为等效的粘滞阻尼,其在MATi材料定义中通过参数G指定,用于模拟线性材料的能量损失,与应变成比例。在频率响应和复特征值求解中,结构阻尼会导致复刚度矩阵出现虚数项,而在瞬态求解中则转化为与时间导数成比例的力。 结构阻尼的效果可以直观地通过虚刚度的概念来理解。虚刚度在力与位移的关系中引入了相位滞后,导致力响应沿着椭圆轨迹变化,椭圆包围的面积表示了损失的能量。 动力学分析方法和NX NASTRAN的使用介绍强调了CAE(计算机辅助工程)在现代工程设计中的重要性。随着计算能力的增强和软件的发展,有限元分析已成为产品设计和研发不可或缺的一部分。CAE能够缩短开发周期、减少试验次数和成本,提高产品质量,预测产品性能,进行优化设计,减少材料消耗,以及提前发现潜在问题。NASTRAN作为NASA在1965年开发的有限元分析程序,经过几十年的发展,已经成为全球广泛使用的工具,支持多种复杂的工程分析任务。 阻尼效应在动力学分析中起着关键作用,尤其是在NX NASTRAN软件中,通过不同的阻尼模型可以精确模拟实际工程问题中的能量损耗现象。CAE技术和NASTRAN的结合,极大地推动了工程分析和产品设计的效率与精度。

ImportError: dlopen(/Users/red/Library/Python/3.9/lib/python/site-packages/_cffi_backend.cpython-39-darwin.so, 0x0002): tried: '/Users/red/Library/Python/3.9/lib/python/site-packages/_cffi_backend.cpython-39-darwin.so' (mach-o file, but is an incompatible architecture (have 'arm64', need 'x86_64')), '/System/Volumes/Preboot/Cryptexes/OS/Users/red/Library/Python/3.9/lib/python/site-packages/_cffi_backend.cpython-39-darwin.so' (no such file), '/Users/red/Library/Python/3.9/lib/python/site-packages/_cffi_backend.cpython-39-darwin.so' (mach-o file, but is an incompatible architecture (have 'arm64', need 'x86_64'))thread '<unnamed>' panicked at 'Python API call failed', /Users/runner/.cargo/registry/src/index.crates.io-6f17d22bba15001f/pyo3-0.18.3/src/err/mod.rs:790:5note: run with `RUST_BACKTRACE=1` environment variable to display a backtraceTraceback (most recent call last): File "/usr/local/project/red/python/memory.py", line 3, in <module> import paramiko File "/Users/red/Library/Python/3.9/lib/python/site-packages/paramiko/__init__.py", line 22, in <module> from paramiko.transport import ( File "/Users/red/Library/Python/3.9/lib/python/site-packages/paramiko/transport.py", line 33, in <module> from cryptography.hazmat.primitives.ciphers import algorithms, Cipher, modes File "/Users/red/Library/Python/3.9/lib/python/site-packages/cryptography/hazmat/primitives/ciphers/__init__.py", line 11, in <module> from cryptography.hazmat.primitives.ciphers.base import ( File "/Users/red/Library/Python/3.9/lib/python/site-packages/cryptography/hazmat/primitives/ciphers/base.py", line 10, in <module> from cryptography.exceptions import ( File "/Users/red/Library/Python/3.9/lib/python/site-packages/cryptography/exceptions.py", line 9, in <module> from cryptography.hazmat.bindings._rust import exceptions as rust_exceptionspyo3_runtime.PanicException: Python API call failed

2023-07-08 上传

将下面这段源码转换为伪代码:def bfgs(fun, grad, x0, iterations, tol): """ Minimization of scalar function of one or more variables using the BFGS algorithm. Parameters ---------- fun : function Objective function. grad : function Gradient function of objective function. x0 : numpy.array, size=9 Initial value of the parameters to be estimated. iterations : int Maximum iterations of optimization algorithms. tol : float Tolerance of optimization algorithms. Returns ------- xk : numpy.array, size=9 Parameters wstimated by optimization algorithms. fval : float Objective function value at xk. grad_val : float Gradient value of objective function at xk. grad_log : numpy.array The record of gradient of objective function of each iteration. """ fval = None grad_val = None x_log = [] y_log = [] grad_log = [] x0 = asarray(x0).flatten() # iterations = len(x0) * 200 old_fval = fun(x0) gfk = grad(x0) k = 0 N = len(x0) I = np.eye(N, dtype=int) Hk = I old_old_fval = old_fval + np.linalg.norm(gfk) / 2 xk = x0 x_log = np.append(x_log, xk.T) y_log = np.append(y_log, fun(xk)) grad_log = np.append(grad_log, np.linalg.norm(xk - x_log[-1:])) gnorm = np.amax(np.abs(gfk)) while (gnorm > tol) and (k < iterations): pk = -np.dot(Hk, gfk) try: alpha, fc, gc, old_fval, old_old_fval, gfkp1 = _line_search_wolfe12(fun, grad, xk, pk, gfk, old_fval, old_old_fval, amin=1e-100, amax=1e100) except _LineSearchError: break x1 = xk + alpha * pk sk = x1 - xk xk = x1 if gfkp1 is None: gfkp1 = grad(x1) yk = gfkp1 - gfk gfk = gfkp1 k += 1 gnorm = np.amax(np.abs(gfk)) grad_log = np.append(grad_log, np.linalg.norm(xk - x_log[-1:])) x_log = np.append(x_log, xk.T) y_log = np.append(y_log, fun(xk)) if (gnorm <= tol): break if not np.isfinite(old_fval): break try: rhok = 1.0 / (np.dot(yk, sk)) except ZeroDivisionError: rhok = 1000.0 if isinf(rhok): rhok = 1000.0 A1 = I - sk[:, np.newaxis] * yk[np.newaxis, :] * rhok A2 = I - yk[:, np.newaxis] * sk[np.newaxis, :] * rhok Hk = np.dot(A1, np.dot(Hk, A2)) + (rhok * sk[:, np.newaxis] * sk[np.newaxis, :]) fval = old_fval grad_val = grad_log[-1] return xk, fval, grad_val, x_log, y_log, grad_log

2023-06-06 上传