动力分析模型调试:提升有限元模型准确性的关键步骤

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本章节主要探讨了动力分析模型调试在数字视频和高清算法及接口(第二版)中的重要性,特别是在有限元模型的应用中。它强调了在设计过程中通过系统检查和归档确保模型的一致性和合理性,以及如何在模型准备和分析阶段避免常见问题。以下是一些关键知识点: 1. **模型检查与归档**: - 在有限元模型的制作和传递过程中,需要进行系统性的检查,确保模型满足不同级别的分析验证和归档要求。这不代替独立的分析验证,而是用来提前发现并修正建模错误。 2. **建模要点**: - 没有一个全面的检查清单,但推荐使用简单的验证方法,如预估等效梁或质量系统的测试结果,帮助识别冗余和预测结果。 - 建模初期,应避免实体元,优先使用梁元和板元;简化RBE2s和RBE3s;减少偏移和局部细节;忽略次要不连续性。 - 后续模型细化中,要关注薄板的弯曲能力和细长构件的动态稳定性,使用膜属性的销接杆分析检测奇异性和避免AUTOSPC。 3. **结果评估**: - 重视载荷和路径的物理重要性,注意力矩偏移和模型对刚性路径的影响。应力分析需细致到部件级别,可能需要调整模型特性以符合实验数据或动力特性。 4. **动力学分析方法与NASTARAN**: - 数值模拟技术,特别是有限元分析,随着计算机技术的发展而兴起,CAE(计算机辅助工程)成为工程设计的重要工具,NASTRAN由NASA开发,是广泛应用的有限元分析系统。 5. **CAE的优势**: - CAE仿真在产品研发中的作用显著,包括缩短开发周期、降低成本、提高产品质量、优化设计和预防潜在问题等。 6. **模型精细度与质量考虑**: - 动力分析中,对质量分布的精确处理至关重要,尤其是对于局部响应,必须确保足够的质量点和适当的弹性单元,同时在ASET集中。 7. **软件背景与历史**: - NASTRAN的历史悠久,自20世纪60年代开发以来,经历了多个版本,成为了全球广泛使用的有限元分析系统。 本章提供了关于动力分析模型调试的实用建议和策略,旨在提升有限元模型的准确性和效率,适用于NASTRAN这样的高级CAE软件环境下的工程分析。

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