User:Muhamad.akbar41

Nama saya Muhamad Akbar Fuad, nama panggilan Akbar. Saya adalah seorang mantan kepala produksi di sebuah perusahaan manufaktur elektronika di Kota Bogor. Alhamdulillah, saat ini sudah menemukan pekerjaan baru sebagai guru matematika sma. Bidang peminatan yang diambil adalah Sistem Otomasi dan Manufaktur, dengan topik penelitian Additive Manufacturing Systems. Saya memiliki interest akan suatu sistem produksi massal. Didorong dengan pengalaman

1. Menjalankan Mesin-Mesin Produksi
2. Manajemen Inventory Perusahaan 

sebagai seorang kepala produksi membuat pemikiran terbaru untuk mengoptimalkan kehandalan Produksi dan Manajerial Keuangan Perusahaan. Pengalaman bekerja selama 1,5 tahun ,ternyata, membuka realitas hidup bahwa PHK itu TIDAK LEPAS dari resiko-resiko yang mungkin dialami oleh masing-masing pegawai perusahaan. Oleh karenanya, tujuan utama mengapa saya mempelajari materi Komputasi Teknik adalah untuk

1. mengoptimalkan ketahanan produksi unit usaha
2. mencegah angka PHK yang lebih meluas lagi

ditengah ketidakpastikan ekonomi global dan kondisi perpolitikan nasional.

Diharapkan, ilmu-ilmu tentang komputasi teknik yang akan saya pelajari mampu membawa angin segar untuk perusahaan-perusahaan lainnya dalam mempertahankan usahanya dan meminimalisir angka PHK ditengah ketidakpastian ekonomi saat ini. Cukuplah hanya saya yang di rumahkan, saya hanya tidak ingin melihat angka PHK kembali meningkat.  

BELAJAR KOMPUTASI TEKNIK DENGAN CHAT GPT

DAI5

Conscious Thinking (Think about Reality and How to Solve it all)

I(2) Intention
I(3) Initial Thinking
I(4) Idealization
I(5) Instruction Set

JILID 1 : 1-Dimensional Partial Differential Equation (PDE)

Question 1: Did you know about DAI5?

The DAI5 Framework is a structured method designed to support systematic problem-solving, particularly in engineering and technical analysis. Developed by Dr. Ahmad Indra Siswantara, the DAI5 framework consists of five main steps: defining the problem, analyzing causes, ideating solutions, implementing, and evaluating outcomes. This approach is often applied in complex scenarios like numerical simulations, finite element analysis, and stress testing within engineering fields. By using DAI5, users aim to ensure each phase is rigorously analyzed to optimize solutions and outcomes, as demonstrated in various technical case studies on topics such as fluid dynamics and pipe stress analysis.

Question 2: Can you derive finite element equations from 1D PDE governing equations using weighted residual in a very simple way along with an example?

Certainly! Deriving the finite element equations from a 1D partial differential equation (PDE) using the weighted residual method is a great way to understand the basics of the finite element method (FEM). Let’s go through it step-by-step with a simple example.

Problem Setup: 1D PDE Example Consider the 1D steady-state heat conduction equation with no internal heat generation:

where:

•	u(x) is the temperature field,
•	k is the thermal conductivity (assumed constant for simplicity),
•	L is the length of the domain.

Suppose we have the boundary conditions:

1.	u(0)=u0 (a Dirichlet boundary condition),
2.	du/dx = q at x = L (a Neumann boundary condition).

Step 1: Formulate the Weak Form (Weighted Residual Form) To derive the finite element equations, we start with the weak form of the governing equation. This involves:

1.	Multiplying the differential equation by a test function v(x),
2.	Integrating over the domain,
3.	Applying integration by parts to reduce the order of derivatives on u.

The weighted residual form is:

Using integration by parts to move the derivative from u to v, we get:

The boundary term,[v(x).k.du/dx]L0 , will incorporate boundary conditions:

•	At x=0, v(0)=0 due to the Dirichlet boundary condition (since u(0)=u0 is known).
•	At x=L, we have the Neumann boundary condition du/dx=q.

This leaves us with:

Step 2: Discretize the Domain and Approximate u(x) Now, we approximate u(x) using finite element shape functions. Suppose we divide the domain into two linear elements, and approximate u(x) as:

u(x) = u1.N1 (x) + u2.N2 (x)

where:

•	N1(x) and N2(x) are linear shape functions,
•	u1 and u2 are the nodal values of u at nodes 1 and 2.

For a linear element over a small interval [x1,x2], the shape functions can be written as:

Step 3: Apply the Weighted Residual Method to Each Element For each element, we substitute the approximated u(x) and v(x) (chosen as the shape functions) into the weak form.

1.	Evaluate the integrals: Substitute 

2.	Compute the stiffness matrix entries for each element:

For a linear element, this integral simplifies to a constant and can be calculated based on the properties of the shape functions.

3.	Assemble the Global System of Equations: After computing K for each element, assemble them into a global stiffness matrix.

4.	Apply Boundary Conditions to solve for the unknown nodal values.

Summary

This procedure gives you a system of linear equations:

where:
•	K is the global stiffness matrix,
•	U is the vector of unknown nodal values,
•	F is the force vector, which includes contributions from the Neumann boundary condition.